CBSE Class 12 Physics Revision Notes Chapter 5

Class 12 Physics Chapter 5 Notes – Magnetism and Matter

Physics requires one to have a solid conceptual understanding of all the concepts. It is interlinked with Physics and Chemistry and hence becomes a subject of utmost importance.

The Class 12 Physics Chapter 5 ‘Magnetism and Matter’ is the study of the charges and their magnetic properties. One can study in detail about magnetism in this chapter. The vital topics covered in Chapter 5 Physics Class 12 notes include:

• The bar magnet
• Magnetism and gauss’s law
• The Earth’s magnetism
• Magnetisation and magnetic intensity
• Magnetic properties of materials 
• Permanent magnets and electromagnets

Everything about the chapter is covered in-depth in the Class 12 Physics Chapter 5 notes. Also, one will get a clear conceptual understanding after referring to them thoroughly and consistently.

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Key Topics Covered in Class 12 Physics Chapter 5 Notes

CBSE Class 12 Physics Chapter 5 notes cover all about moving charges and Its magnetism.

This chapter is all about magnets and their properties. One should have command over Magnetic Physics to excel in this chapter.

This chapter will help students in developing an interest in Physics. Due to this, they will start enjoying the subject. The entire chapter is covered thoroughly in the Class 12 Physics Chapter 5 notes and is available on the Extramarks website. 

After completing the notes of Class 12 Physics Chapter 5, students will learn to analyse a concept with a better approach and be able to solve questions related to it quickly.

INTRODUCTION TO MAGNETISM 

Magnets! Undoubtedly, its behaviour will attract everyone. The world enjoys the benefits of living a modern and luxurious life. The study of magnets has fascinated scientists worldwide for many centuries, and the door to magnet research is still open today.

Magnetism exists everywhere, from tiny particles like electrons to the entire universe. Historically, Q”magnetism” derives from iron ore magnetite (Fe3O4). In ancient times, magnets were used as a magnetic compass for navigation, magnetic therapy for treatment, and magic shows.

Magnetism is the phenomenon by which certain substances attract parts made of steel, iron, nickel, etc. Freight, super express trains mainly abroad, refrigerators, etc.

Magnetite is the world’s first magnet. That is also known as a natural magnet. Although magnets occur naturally, we can also impart magnetic properties to a substance. In this case, it would be an artificial magnet.

Nowadays, many things that we use in our daily life contain magnets. Some examples include engines, bicycle dynamos, speakers, magnetic tapes for audio and video recordings, mobile phones, headphones, CDs, flash drives, laptop hard drives, refrigerator doors, and generators.

Both electricity and magnetism were once thought to be two independent branches of Physics. In 1820, H.C. Oersted observed a magnetic compass needle’s deflection near a live wire. That united the two disparate branches, electricity and magnetism, into a single subject of “electromagnetism” in Physics.

This unit teaches the basic concepts of magnets and their properties. Later it will be shown how a current-carrying conductor (here, only constant current will be considered, not a time-varying current) behaves like a magnet.

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Earth’s magnetic field and magnetic elements 

The Earth behaves like a magnet. When a bar magnet hangs freely, it points in the NS direction. When two north poles meet, they repel each other. A similar effect will also be observed at the South Pole.

However, if the North Pole and the South Pole are brought together, they attract each other. Magnetic monopoles do not exist, meaning we cannot have a magnet with only the North Pole or the only South Pole. When a bar magnet has broken in half, we get two similar bar magnets with weaker properties. With the help of iron and its alloys, we can make magnets.

From the sports completed in decreased classes, you may have observed that the needle in a magnetic compass or freely suspended magnet involves relaxation in a role that’s about alongside the geographical north-south path of the Earth. 

The north pole of the magnetic compass needle will attract in the direction of the magnetic south pole of the Earth that’s close to the geographic north pole. Similarly, the south pole of the magnetic compass needle will attract in the direction of the magnetic north pole of the Earth that’s close to the geographic south pole. The Physics department,  which deals with the Earth’s magnetic Discipline, is called Geomagnetism or Terrestrial magnetism. 

Three portions are required to specify the Earth’s magnetic discipline on its floor, which might be frequently referred to as the factors of the Earth’s magnetic field. They are 

(a) magnetic declination (D) 

(b) magnetic dip or inclination (I) 

(c) the horizontal aspect of the Earth’s magnetic discipline (BH).  

Day and night time arise because Earth spins approximately on an axis referred to as the geographic axis. A vertical aircraft passing through the geographic axis will be referred to as the geographic meridian. An excellent circle perpendicular to Earth’s geographic axis is called the geographic equator. 

The instantaneous line which connects the magnetic poles of Earth is called the magnetic axis. A vertical aircraft passing through a magnetic axis will be referred to as a magnetic meridian. An excellent circle perpendicular to Earth’s magnetic axis will be referred to as a magnetic equator. 

When the magnetic needle freely suspends, the alignment of the magnet no longer precisely lies alongside the geographic meridian. The perspective among magnetic meridians at a factor and geographical meridian will refer to the declination of magnetic declination (D). At better latitudes, the declination is more, while close to the equator, the declination is smaller. In India, the declination perspective may be minimal, and for Chennai, the magnetic declination perspective will –1° 16ʹ (that’s negative (west)).

The perspective subtended using the Earth’s overall magnetic discipline B with the horizontal path within the magnetic meridian will be referred to as dip or magnetic inclination (I) at that factor. For Chennai, the inclination perspective is 14° 28ʹ. The aspect of Earth’s magnetic discipline alongside the horizontal path within the magnetic meridian will  be referred to as the flat part of Earth’s magnetic discipline, denoted by BH. 

Let BE be the internet Earth’s magnetic discipline at any factor at the floor of the Earth. BE may resolve into perpendicular components.

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• At the magnetic equator

The Earth’s magnetic field will parallel to the Earth’s surface (i.e. horizontal), which implies that the magnetic compass needle rests horizontally at an inclination angle of  I = 0°

BH = BE

BV = 0

That implies the horizontal component will be maximum at the equator, and the vertical part will be zero.

• At the magnetic poles

The Earth’s magnetic field will be perpendicular to the Earth’s surface (i.e.vertical), which implies that the magnetic compass needle rests vertically at an inclination angle  I = 90°. thus

BH = 0

BV = BE

That implies the vertical component will be maximum at the poles, and the horizontal part is zero at the poles.

Basic properties of magnets 

Some basic terminologies and properties to describe the bar magnet.

• Magnetic dipole moment

Consider a bar magnet like the one shown in Figure 3.6. Let qm be the opposing force of the magnetic pole and  l be the distance between the geometric centre of the bar magnet O and one end of the rod. The magnetic dipole moment will be defined as the product of its pole strength and magnetic length. That is a vector quantity denoted by  pm.  d is the vector drawn from the south pole to the north pole, and it’s absolute value d l = 2. The SI unit for the magnetic moment is Am2. The direction of the magnetic moment is from the south pole to the north pole.

• Magnetic Field

The magnetic field is the region or space around any magnet where its influence will feel when holding another magnet in that region. The magnetic field B at a point is defined as a force experienced by the bar magnet with a polar unit of force = 1 (3.5). Its unit is NA-1m-1.

• Types of Magnets

Magnets will divide into natural magnets and artificial magnets. For example, iron, cobalt, nickel etc. They are natural magnets. The forces of natural magnets are feeble, and the shapes of the magnet are irregular. Artificial magnets are manufactured to have the desired shape and strength. If the magnet is rectangular or cylindrical,  it is called a bar magnet.

• Properties of the Magnet

 Below are the properties of the bar magnet.

1. 1 . A freely hanging bar magnet always points in a north-south direction.
2. A magnet attracts or repels another magnet or magnetic substance. The attraction or repulsion force is greatest near the end of the bar magnet. When a bar magnet will dip in an iron spatula, they stick to the ends of the magnet.
3. When a magnet has broken into pieces, each piece behaves like a magnet with poles at its ends.
4. Two poles of a magnet have the same polarity as each other.
5. The length for the bar magnet is called the geometric length, and the length between two magnetic poles on a bar magnet is called the magnetic length. The magnetic length will always be slightly smaller than the geometric length
   

• Magnetic field lines

We observe a pattern when iron infills will spray onto a pane of glass placed on a short bar magnet. The way indicates that the magnet will have two poles. That is a visual representation of magnetic field lines. Therefore, the magnetic field lines are imaginary magnetic field lines in and around the magnet.

Some of the properties of  magnetic field lines are:

1. The y-lines are continuous; outside the magnet, the field lines originate at the north pole and end at the south pole.
2. They form closed loops that traverse the interior of the magnet. But here, the lines appear to start at the South Pole and end at the North Pole to form closed loops.
3. A more significant number of adjacent lines indicates a stronger magnetic field.
4. The lines do not cross.
5. The tangent drawn to the field line indicates the direction of the field at that point.
6. Magnetic field lines are continuous closed curves. The direction for the magnetic field lines is outside the magnet from the north pole to the south pole and inside the magnet from the south pole to the north pole.
7. The direction of the magnetic field at any point on the curve will be known by drawing tangents to the magnetic field lines.
8. Magnetic field lines never cross. Otherwise, the magnetic compass needle would point in two directions, which is impossible. The field lines’ degree of proximity determines the magnetic field’s relative strength. The magnetic field is vital where the magnetic field lines crowd together and weak where the magnetic field lines are far apart.

The analogy of Magnetic field lines with Electrostatics:

Source: Internet

• Magnetic Flux

The number of magnetic field lines crossing any surface is usually defined as the magnetic flux ΦB through the surface. Mathematically, the magnetic flux is given through  ​​area  A in a homogeneous magnetic field  B. θ is the angle between  B and  A.

• Special cases

1. if B is perpendicular to the surface, i.e. θ = 0°, the magnetic flux is ΦB = BA (maximum). If  B is parallel to the surface, θ = 90°, the magnetic flux is ΦB = 0. Assuming that the magnetic field is not uniform across the surface, it can be written as ΦB = ∫ B A.d
2. The magnetic flux is a scalar quantity. The SI unit for magnetic flux is the Weber, denoted by the symbol Wb. The CGS unit of magnetic flux will be Maxwell. 1 Weber = 108 Maxwell
3. The magnetic flux density will be defined as the number of intersecting magnetic field lines per unit area perpendicular to the direction of the lines of force. Its unit is Wb m-2 or Tesla (T).
4. Uniform magnetic field and nonuniform magnetic field

• Uniform magnetic field

A magnetic field is uniform when it has the same magnitude and direction at all points in a given region. For example, the Earth’s magnetic field is locally uniform. The Earth’s magnetic field has equal value in the entire area of ​​your school!

• Nonuniform Magnetic Field

The magnetic field is non uniform when the magnitude, direction, or both vary in different regions. Example: magnetic field of a bar magnet.

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COULOMB’S INVERSE SQUARE LAW OF MAGNETISM 

Consider bar magnets A and B. When magnet A’s north pole and magnet B’s north pole or the south pole of magnet A and magnet B are delivered closer, they repel each other. 

On the other hand, while the north pole of magnet A and the south pole of magnet B or magnet A and the north pole of magnet B is delivered closer, their bars entice each other. 

That appears like Coulomb’s regulation for fixed costs studied in Unit I (contrary prices entice and prefer costs repel every other). So analogous to Coulomb’s law in Electrostatics, we will also learn about Coulomb’s law for magnetism.

The pressure of appeal or repulsion among magnetic poles is proportional to the manufactured from their pole strengths and inversely proportional to the rectangular space among them.

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Magnetic discipline at a factor alongside the axial line of the magnetic dipole (bar magnet) 

Consider a bar magnet NS. Let N be the north pole and S be the south pole for the bar magnet. Every pole of electricity qm is separated by a distance of 2l. The magnetic discipline at a factor C (lies alongside the magnet’s axis) at a distance r from the geometrical centre O of the bar magnet may be computed via means of retaining unit north at C. 

The magnetic discipline at C because the north pole is the space between the north pole of the bar magnet as well as the unit north pole at C. 

The magnetic discipline at C because of the south pole. This (r + l) is the space between the bar magnet’s south pole and the unit north pole at C.

The net magnetic field is due to the magnetic dipole at point C.

when the distance between two poles in a bar magnet is small (looks like a short magnet), compared with the distance between the geometric centre O of the bar magnet and the position of the point C.

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The magnetic field along a point of the equator by a magnetic dipole (bar magnet)

Consider an NS bar magnet. Let N be the north pole and S the south pole of the bar magnet, each with an opposing force qm and separated by a distance of 2l. The magnetic field at a point C (it lies along the equator) at a distance r from the geometric centre O of the bar magnet can be calculated by keeping the unit north pole at C.

The magnetic field at C due to the south pole is not equal to the net magnetic field at point C due to the dipole.

Suppose the distance between two poles in a bar magnet is small (it looks like a short magnet). Compare this with the distance between the bar magnet’s geometric centre O and point C’s locus.

Note that the magnitude of Biaxial is twice that of Equatorial, and the direction of Biaxial and Equatorial are opposite. 

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TORQUE ACTING ON A BAR MAGNET IN A UNIFORM MAGNETIC FIELD

Consider a magnet of length 2l and pole strength qm held in a uniform magnetic field  B. Each pole experiences the force of magnitude qmB but acts in opposite directions. Hence, the net force exerted on the magnet will be zero; hence, there is no translational motion. These two equal and opposite forces form a pair (around the centre of the bar magnet) and tend to align the magnet in the direction of the magnetic field B—the force experienced by the north pole.

The potential energy for the bar magnet in a uniform magnetic field

When a bar magnet (magnetic dipole) with dipole moment pm is held at an angle θ with the direction of the uniform magnetic field B, the torque acting on the dipole is considerable.

That work is stored like potential energy in a bar magnet with an angle θ (on rotation from θ’ to θ). 

The potential energy difference between the angular positions θ’ and θ. Suppose we choose the reference point with θʹ = 90  so that the second term of the equation is zero.

From the two previous results, we conclude that the potential energy of the bar magnet is minimal when aligned with the external magnetic field and is at its maximum when the bar magnet is aligned antiparallel to the external magnetic field.

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MAGNETIC PROPERTIES

All materials are inherently non-magnetic. Also, not all magnetic materials behave the same way. Some basic parameters are used to distinguish one magnetic material from another.

When such a material is held in an external magnetic field, atomic dipoles are induced When such material is stored in an external magnetic field. Atomic dipoles are induced.

The magnetic field magnetising a sample or specimen is called the magnetising field. The magnetising field is a vector quantity and is denoted by H.

•  Magnetic Permeability

Magnetic permeability is the measure of the material’s ability to allow magnetic field lines to pass, the substance’s ability to absorb magnetisation, or the degree of penetration of the magnetic field by the substance.

In free space, the permeability (or absolute permeability) is denoted by μ0 and for any other medium by μ. The relative permeability μr will be defined as the ratio between the medium’s absolute permeability and free space’s permeability.

The relative permeability is a dimensionless number as well as has no units. For free space (air or vacuum), relative permeability will be unity, i.e. H. µr = 1.

•   Magnetisation Intensity 

Any bulk material (any object of finite size) contains many atoms. Each atom is made up of electrons undergoing orbital motion. Because of the orbital motion, the electron has a magnetic moment, a vector quantity. In general, these magnetic moments are randomly aligned. Hence the net magnetic moment is zero per unit volume of material.

When such a material is placed in an external magnetic field, atomic dipoles are induced and therefore try to align partially or entirely along the direction of the external field. The net magnetic moment per material unit is known as the magnetisation intensity. It’s a vector size.

The SI unit of magnetisation intensity is the ammeter. For a bar magnet with polar force qm, length 2l and cross-sectional area  A.

This means for a bar magnet, The strength of the magnetisation can be defined as the strength of the pole per unit area (face area).

•   Magnetic induction or total magnetic field

The substance is magnetised when a substance such as B., a soft iron rod, is placed in a uniform magnetic field H. The magnetic induction (total magnetic field) within sample B is equal to the sum of the magnetic field B generated in a vacuum due to the magnetising field and the magnetic field Bm due to the induced magnetism of the substance.  

•  Magnetic susceptibility

When a substance is held in a magnetising field  H, the magnetic susceptibility provides information about how a material responds to the external (applied) magnetic field. In other words, magnetic susceptibility measures how easily and strongly a material can be magnetised. It will be defined as the ratio between the material’s magnetisation strength M induced in the magnetising field.  

It is a dimensionless quantity. The magnetic susceptibility for some of the isotropic substances is given.

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CLASSIFICATION OF MAGNETIC MATERIALS

Magnetic materials are usually classified into three types based on their behaviour in a magnetising field. They are diamagnetic, paramagnetic and ferromagnetic materials.(a) Diamagnetic materials

The orbital motion for electrons around the nucleus creates a magnetic field perpendicular to the plane of the orbit. Therefore, each electron orbit has a finite orbital magnetic dipole moment. Hence the orbital planes of the other electrons are randomly oriented, the vector sum of the magnetic moments will be zero, and there is no net magnetic moment for each atom.

In the presence of a uniform external magnetic field, some electrons will speed up, and some will slow down. Electrons whose moment was antiparallel are accelerated according to Lenz’s law and produce an induced magnetic moment in the opposite direction to the field. The induced moment vanishes as soon as the external field is removed.

When placed in a nonuniform magnetic field, the interaction between the induced magnetic moment and the external field creates a force that tends to move the material from the more substantial part of the external field to the weaker position. This means that the area repels the diamagnetic material.

This action is called diamagnetic action, as such materials are known as diamagnetic materials. Examples: bismuth, copper and water, etc. The properties of diamagnetic materials are

1. i) The magnetic susceptibility is negative.
2. ii) The relative permeability is slightly less than one.

iii) Magnetic field lines are repelled or ejected by diamagnetic materials when placed in a magnetic field.

1. iv) Susceptibility is almost independent of temperature.

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•   Paramagnetic Materials

Each atom or molecule has a net magnetic dipole moment in some magnetic materials, the vector sum of the electrons’ spin and orbital magnetic moments. Due to the random orientation for these magnetic moments, the net magnetic moment of the materials will be zero.

In the presence of an external magnetic field, the torque acting on the atomic dipoles orients them in the direction of the area. As a result, a net magnetic dipole moment is induced in the order of the applied field. The induced dipole moment exists as long as the external field exists.

When paramagnetic materials are placed in a nonuniform magnetic field, they move from the weakest to the most vital part of the field. Materials that exhibit weak magnetism in the direction of the applied field are known as paramagnetic materials—examples: aluminium, platinum, chromium and oxygen etc.

The properties of paramagnetic materials are:

1. i) The magnetic susceptibility is positive and small.
2. ii) The relative permeability is more significant than one. iii) Magnetic field lines attract paramagnetic materials when placed in a magnetic field.
3. iv) The susceptibility is inversely proportional to the temperature.

Curie’s Law

As temperature increases, thermal vibration changes the orientation of the magnetic dipole moments. Therefore, the magnetic susceptibility decreases with increasing temperature.

This relationship is known as Curie’s law. Here C is called the Curie constant, and the temperature T is given in Kelvin. The graph of magnetic susceptibility versus temperature is a rectangular hyperbola.

•   Ferromagnetic Materials

An atom or molecule in a ferromagnetic material possesses a net magnetic dipole moment as in a paramagnetic material. A ferromagnetic material consists of smaller areas called ferromagnetic domains (Figure  ). Within each domain, the magnetic moments spontaneously align in one direction. This alignment is caused by a strong interaction arising from the spin of the electrons, which depends on the interatomic distance. Every domain has a net magnetisation in one direction. However, the Magnetisation direction varies from domain to domain; thus, the net magnetisation of the sample is zero. In the presence of external magnetic field, two processes take place:

(1) Domains that have magnetic moments parallel to the field increase in size

(2) Other domains (not parallel to the field) are rotated to align with the field.

As a result of these mechanisms, the material’s solid net magnetisation is in the direction of the applied field.

When ferromagnetic materials are placed in a nonuniform magnetic field, they move from the weakest to the most vital part of the field. Materials that exhibit strong magnetism in the direction of the applied field are called ferromagnetic materials—examples: iron, nickel and cobalt. 

Some common differences between Diamagnetic, Paramagnetic and Ferromagnetic substances:

The properties of ferromagnetic materials are:

1. i) The magnetic susceptibility is positive and significant.
2. ii) The relative permeability is large.

iii) Magnetic field lines are strongly attracted to ferromagnetic materials when placed in a magnetic field.

1. iv) The susceptibility is inversely proportional to the temperature. 

Curie-Weiss Law

As temperature increases,  ferromagnetism decreases due to the increased thermal motion of atomic dipoles. At a specific temperature, the ferromagnetic material becomes paramagnetic. This temperature is known as the Curie temperature TC.

This relationship is called the Curie-Weiss law. C is called the Curie constant, and the temperature T is on the Kelvin scale.

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HYSTERESIS

When a ferromagnetic material is held in a magnetic field, the material becomes magnetised by induction. An important property of the ferromagnetic material is that the change of the magnetic induction B with the magnetising field H is not linear. This means that the ratio is not constant. Let’s examine this behaviour in detail.

A ferromagnetic material (e.g. iron) is slowly magnetised by a magnetising field H. The magnetic induction B of the material increases from point A with the size of the magnetic field and then reaches a saturation value. This material response is represented by the path AC. Saturation magnetisation is the maximum point to which the material can be magnetised by applying the magnetising field.

If the magnetic field is reduced, the magnetic induction decreases but does not return to the original path CA. Take a different way than the CD. If the magnetising field is zero, the magnetic induction is non-zero and has a positive value. This implies that some magnetism remains in the sample even at H = 0. The residual magnetism AD present in the sample is called remanence or remanence. Remanence is defined as the ability of  materials to retain  magnetism within themselves

after the magnetising field has disappeared.

The magnetic field gradually increases in the opposite direction to demagnetise the material. Now the magnetic induction along DE decreases and becomes zero at E. The magnetisation field AE is required in the opposite direction to bring the residual magnetism to zero. The magnitude of the reverse magnetising field at which the residual magnetism of the material disappears is called coercivity.

Further increasing H in the reverse direction causes the magnetic induction to increase along EF until it saturates at F in the reverse order. When the magnetic field decreases and increases in the reverse direction, the magnetic induction follows the FGKC pathway, this closed curve ABCDEFGH is called the hysteresis loop and corresponds to one magnetisation cycle.

The magnetic induction B lags behind the magnetising field H throughout the cycle. This phenomenon of magnetic induction lagging behind the magnetic field is called hysteresis. Hysteresis means “lagging”.

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• Hysteresis Loss:

During the sample’s magnetisation through one cycle, energy is lost in the form of heat. That loss is attributed to the rotation and orientation of the molecular magnets in different directions. It has been found that the energy lost (or dissipated) per unit volume of material as it is carried through a magnetisation cycle is equal to the area of ​​the hysteresis loop.

• Hard and soft magnetic materials

Depending upon the shape and size of the hysteresis loop, ferromagnetic materials are divided into soft magnetic materials with a smaller area and hard magnetic materials with a larger area. The comparison of the hysteresis loops for the two magnetic materials. Differences between soft and hard ferromagnetic materials p.No. Features Soft Ferromagnetic Materials Hard Ferromagnetic Materials 

1 When the external field is removed, magnetisation disappears. Magnetisation remains 

2 Loop area Small Large 

3 Remanence Low High 

4 Coercivity Low High 

5 Magnetic susceptibility and  permeability High Low 

6 Hysteresis loss Less More 

7 Uses magnetic core, transformer core and electromagnets permanent magnets

8.Examples are soft iron, mumetal, alloy, carbon steel, alnico, magnetite etc.

Susceptibility and energy loss during a magnetisation cycle for each ferromagnetic material. Therefore, studying the hysteresis loop helps us to choose the right and suitable material for a specific purpose. 

1. i) Permanent magnets:

Materials with high remanence, high coercivity and low permeability are suitable for manufacturing permanent magnets. Examples: Carbon and Alnico Steel

1. ii) Electromagnets:

Materials with high initial permeability, low remanence, low coercivity, and thin hysteresis loop with the smaller area are preferred for making electromagnets. Examples: soft iron and mu-metal (nickel-iron alloy).

iii) Transformer Core:

Materials with high initial permeability, large magnetic induction, as well as thin hysteresis loop with smaller areas are required to construct transformer cores—examples: Soft iron.

Difference between permanent magnets and electromagnets:

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MAGNETIC EFFECTS OF CURRENT Oersted’s experiment

Hans Christian Oersted noticed in 1820 while preparing for his Physics lecture, that an electric current flowing through a wire deflects the nearby magnetic needle in the compass. Through careful investigation, he found that the deflection of the magnetic needle is due to the change in the magnetic field generated around the current-carrying conductor. When the current direction is reversed, the magnetic needle deflects in the opposite direction. This led to the development of the “electromagnetism” theory, which combined two branches of Physics, namely electricity and magnetism.

Magnetic field around a straight current-carrying conductor and a circular loop

(a) Straight current-carrying conductor:

Suppose we hold a magnetic compass near a straight current-carrying conductor. The magnetic compass needle experiences a torque and is deflected to move at that point to align in the direction of the magnetic field. By following the direction indicated by the magnetic needle, we can draw the magnetic field lines at a distance. In a straight current-carrying conductor, the magnetic field is made up of concentric circles that have their common centre on the axis of the conductor. 

 The direction of the circular magnetic field lines is clockwise or counterclockwise, depending on the direction of the current in the conductor. As the strength (or magnitude) of the current increases, the density of the magnetic field also increases. The power of the magnetic field (B) decreases with increasing distance (r) from the conductor.

(b) Current-carrying circular coil:

Suppose we hold a magnetic compass near a current-carrying circular conductor. The magnetic compass needle experiences a torque and is deflected to align itself in the direction of the magnetic field at this point. At points A and B near the coil, we can see that the magnetic field lines are circular. The magnetic field lines will almost parallel each other near the centre of the loop, indicating that the field is virtually uniform near the centre of the coil.

The magnetic field’s strength increases as the coil’s current increases, the number of turns increases, or both. The polarity (the North Pole or the South Pole) depends on the current direction in the loop.

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Right Thumb Rule

The right-hand rule will be used to find the direction of the magnetic field when the direction of the current in a conductor is known. Suppose we hold the current-carrying conductor in the right hand so that the thumb points in the direction of the current flow, and then the fingers surrounding the conductor point in the order of the generated magnetic field lines.

Maxwell’s Right Corkscrew Rule

This rule can also be used to determine the direction of the magnetic field around the current-carrying conductor. If we turn a right-hand screw with a screwdriver, then the direction of the current is the same as the direction the screw is advancing, and the rule of rotation of the screw indicates the direction of the magnetic field. 

BIOT – SAVART’S LAW

Shortly after Oersted’s discovery, both Jean-Baptiste Biot and Felix Savart performed quantitative experiments in 1819  on the force experienced by a magnet held near a current-carrying wire and came to a mathematical result expression that gives the magnetic field at a specific point in space to the current that the magnetic field produces. This applies to any form of leader. Definition and explanation of the Biot-Savart law

Biot and Savart observed the magnitude of the magnetic field dB at a point P at a distance r from the small element length of a current-carrying conductor. 

(i) varies directly as the  current intensity I

(ii) directly as the absolute value of the length element dl 

(iii) directly as the sine of the angle θ between dl and r.

(iv) inverse to the square of the distance r between the point P and the element of length dl.

Cases

1. If the point P lies on the conductor, then θ = 0. Therefore, dB is zero.
2. If the point is perpendicular to the conductor, then θ = 90. Therefore, dB is maximum.

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Similarities between electric field (from Coulomb’s law) and magnetic field (from Biot-Savart’s law)

Electric and magnetic fields

• obey the inverse square law, so they are long-range fields.
• They obey the principle of superposition and are linear  to the source in terms of magnitude  

Differences are seen between the electric field (from the Coulomb law) and the magnetic field (from the Biot-Savart law).

Magnetic field due to a long straight current-carrying conductor 

To calculate the magnetic field at a point P  at a distance from the wire,  consider a small line element dl (distance AB). The magnetic field at a point of P due to the current element Idl can be calculated from the Biot-Savart law.

Here nˆ is the vector unit that shows the page at P, θ is the angle between the current element Idl and the line connecting dl and point P. Let r be the distance from the line element at A to point P.

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The magnetic field generated along the axis of a current-carrying circular coil

Consider a current-carrying circular helix of radius R and let I be the current flowing through the wire in the direction.

The magnetic field at a point P around the axis of the circular coil at a distance z from the centre of the coil O is calculated by taking two opposed linear elements of the loop, each of length dl at C and D. Let r be the vector connecting the current element at C and the point P. According to the Biot-Savart law, the magnetic field at P is due to the current part at C.

The magnitude of the magnetic field at P due to the current element at D is the same as that of the element at C because the distances from the coil are equal. But your direction is along PS.

The magnetic field due to each current element splits into two components; dBcosφ along the y-direction and dBsinφ along the z-direction. The horizontal components cancel out, while the vertical parts (dBsinφk ) alone contribute to the net magnetic field.   

If we integrate the linear element from 0 to 2πR, we get the net magnetic field B at point P due to the circular loop current flowing through it. 

Tangent law and tangent galvanometer

The tangent galvanometer is a device for detecting tiny currents. It is a moving magnet-type galvanometer. Its functionality is based on the tangent law.

• Law of Tangent 

Suppose a compass needle or magnet is suspended freely in two uniform magnetic fields perpendicular to each other. In that case, it will stop in the direction of the resultant of the two fields.

Let B be the magnetic field created by passing a current through the tangent galvanometer coil and BH be the horizontal component of the Earth’s magnetic field. Under the action for two magnetic fields, the needle stops at an angle θ with BH such that B = BH tan θ

• Construction

A tangential galvanometer (TG) consists of a copper coil with several turns placed on a non-magnetic round frame. The frame is made of brass or wood, mounted vertically on a horizontal base table (round table) with three levelling screws. The TG is provided with two or more coils with different numbers of turns. Most of the equipment in the lab contains 2-turn, 5-turn, and 50-turn coils of different thicknesses used to measure currents of various magnitudes.

In the centre of the turntable is a small vertical ledge on which a compass box is placed. The compass body consists of a small magnetic needle that rotates at its centre so that the centres of the magnetic hand and the circular coil coincide exactly. A thin aluminium pointer, mounted perpendicular to the magnetic needle, moves on a graduated circular scale. The circular scale will be divided into four quadrants, and they are divided into degrees. Each quadrant is numbered from 0° to 90° to avoid parallax errors in the measurement; a mirror is placed under the aluminium pointer.

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Precautions

1. All nearby magnets and magnetic materials are kept away from the instrument.
2. Using a spirit level, adjust the levelling screws on the base so that the tiny magnetic needle is horizontal and the coil (mounted on the frame) is vertical.
3. The plane of the coil will keep parallel with the small magnetic needle by rotating the ring about its vertical axis. So, the loop stays on the magnetic meridian.
4. Only the compass case is turned so that the aluminium pointer shows 0.

Theory

In the divergent galvanometer experiment, the small magnetic needle lies along the Earth’s magnetic field’s horizontal component when no current flows through the coil. When the circuit is closed,  electric current flows through the circular loop, creating a magnetic field in the centre of the coil. Now there are two interacting fields perpendicular to each other.

They are:

(1) the magnetic field (B) due to electric current in the coil acting perpendicular to the plane of the coil.

(2) the horizontal component of the Earth’s magnetic field (BH)

An angle θ deflects the rotated magnetic needle through these transverse fields. From the tangent, the law follows: B = BH tan θ

When an electric current passes through a circular coil of radius R and N turns, the magnitude of the magnetic field is at the centre. 

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Current loop as a magnetic dipole

The magnetic field at a point on the axis of the current-carrying circular loop of radius R at a distance z from its centre.

That implies that a current-carrying circular loop behaves like a magnetic dipole with the magnetic moment. Thus, the magnetic dipole moment of any current loop is equal to the product of the current and loop area.

Right-hand rule of thumb 

To determine the direction of the magnetic moment, we use the right-hand rule of thumb, which states that;

If we bend the fingers of the right hand in the direction of the current in the loop, then the extended thumb gives the direction of the magnetic moment associated with the loop.

Magnetic Dipole Moment of the Spinning Electron

Suppose an electron moves in a circle around the nucleus. The electron circulating in a loop is like the current in a circular loop (since the flow of charge makes the current). The magnetic dipole moment is due to a current carrying a circular loop.

When T is the time duration of an electron’s revolution, the current due to the circular motion of the electron is calculated.

The negative sign indicates that magnetic moment and angular momentum are opposite.

The ratio is μL, where L is a constant known as the gyromagnetic ratio. It should be noted that the gyromagnetic ratio is a constant of proportionality connecting the angular momentum for the electron and the magnetic moment of the electron.

According to the Niels Bohr quantisation rule, the angular momentum of an electron moving in a stationary orbit is quantised.

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AMPÈRE’S CIRCUITAL LAW 

Ampères circuital is used to calculate the magnetic field at a point when the problem is symmetric. This is similar to Gauss’ law in Electrostatics.

Ampère’s circular law

Ampère’s law: The line integral of the magnetic field across a closed loop is μ times the net current enclosed by the loop.

The magnetic field through the current-carrying wire of infinite length according to Ampère’s law

Consider a straight current-carrying conductor of infinite length I and the direction of the magnetic field lines. Since the wire is geometrically cylindrical and symmetrical about its axis, we construct a circular ampere loop at a distance r from the centre of the wire.

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Solenoid

A solenoid will be a long coil of wire tightly wound into a spiral. When electric current flows through the solenoid, the magnetic field will create. The solenoid’s magnetic field will be created by the superposition of magnetic fields from each solenoid turn. The rule of the right palm gives the direction of the magnetic field due to the solenoid.

Inside the solenoid, the magnetic field is nearly uniform and parallel to its axis, while the field outside the solenoid is negligibly small. Depending on the direction of the current, one end of the solenoid acts like the north pole, and the other end acts like the south pole.

The current-carrying electromagnet will hold in the right hand. If the fingers are bent in the current direction, the outstretched thumb indicates the direction of the magnetic field of the current-carrying coil. Therefore, a solenoid’s magnetic field is similar to a bar magnet’s magnetic field.

The electromagnet is assumed to be long, which means that the length of the electromagnet is large compared to its diameter. The winding does not always have to be circular. It can also have other shapes. Here we only consider the magnet with circular winding.

Let’s find  the magnetic field at a distant axial point of a solenoid:

Consider the following:

length of the solenoid – 2l

the radius of the solenoid – r

number of turns/unit length – n

Also, consider,

dx – a small element dx in the solenoid

x – a distance of dx from the centre of the solenoid

r – a distance of the point P from the centre of the solenoid O

R is the radius, and x is the distance of the point from the centre of the circular loop.

For a distant axial point, r >> x ; r >> a

Therefore, a2 + (r-x)2= a2 + r2= r2

Therefore, the denominator is (r2) 3/2= r3

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Magnetic field due to a magnetic coil carrying a long current 

Imagine a magnetic coil of length L that has N turns. The diameter of the solenoid is said to be much smaller than its length, and the coil is wound very tightly.

We use Ampere’s circuital law to calculate the magnetic field at any point within the solenoid. Imagine a rectangular loop ABCD.

Since the elementary lengths are along bc and perpendicular to the magnetic field along the solenoid axis, the integrals are likewise. 

Since n is constant for a given magnetic coil and μ0 is also constant. With a fixed current I, the magnetic field in the magnet is also constant.

Toroid

An electromagnet bent so that its ends meet to form a closed ring is called a toroid. The magnetic field has a constant magnitude inside the toroid, while in the inner region (e.g. at point P) and in the outer region (e.g. at point Q), the magnetic field is zero.

(a) Clearance in the toroid

Let’s calculate the magnetic field BP at point P. We construct an ampere loop 1 with radius r1 around point P. For convenience, we’ll take a circular loop, so the length of the loop equals its circumference. 

That is only possible if the magnetic field at point P vanishes.

(b) Open space outside the torus

Let’s calculate the magnetic field BQ at point Q.We construct an ampere loop 3 of radius r3 around point Q.

Since at each turn of the ring circuit, the current leaving the plane of the paper will cancel by the current entering the plane of the paper.

(c) Inside the toroid

Let’s calculate the magnetic field BS at point S by making a loop ampere 2 of construct radius r2 around point S.

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LORENTZ FORCE

When an electric charge q will hold in a magnet at the rest field, no force acts on it. If the charge moves in the magnetic field, it experiences a force simultaneously. This force differs from the Coulomb force. This force will be known as the magnetic force. The equation gives it.

When the charge moves in both the electric and magnetic fields, the total force experienced by the charge will generally give.

Force on a moving charge in a magnetic field 

If an electric charge q moves with velocity v in the magnetic field  B, it experiences a force called the magnetic force  Fm. After careful experiments, Lorentz derived the force experienced by a moving charge in a magnetic field.

1. Fm is directly proportional to the magnetic field B.
2. Fm is directly proportional to the velocity v of the moving charge.
3. Fm is directly proportional to the sine of the angle between the velocity and the magnetic field
4. Fm is directly proportional to the magnitude of the charge q.
5. The direction of Fm is always perpendicular to v and B since Fm is the cross product of v and B.
6. The direction of  Fm with a negative charge is opposite to that of  Fm with a positive charge, provided all other factors are the same, as the picture shows.
7. If the velocity v of charge q is along the magnetic field  B, Fm is zero

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Definition of Tesla:

The strength for the magnetic field is one tesla when a unit charge moves in its unit velocity and experiences unit force. 

The motion of a charged particle in a uniform magnetic field

Consider a charged particle q of mass m moving with velocity in a region with a uniform Magnetic field B enters v ́B such that the velocity is perpendicular to the magnetic field. As soon as the particle enters the field, the Lorentz force acts on it perpendicular to the magnetic field  B and the velocity B.

We conclude that the duration and frequency depend on the charge-to-mass ratio (specific charge) but not on the circular orbit’s speed or radius. If a charged particle moves in an area with a  uniform magnetic field so that its velocity is not perpendicular to the magnetic field, then the particle’s velocity splits into two components; one component is parallel with the field while the other component is perpendicular to the field. The velocity component parallel to the field remains unchanged, and the component perpendicular to the field continues to change due to the Lorentz force. Thus, the particle’s path is not a circle; it is a helix around the field lines. 

For example, the spiral path of an electron as it moves in a magnetic field. Inside the particle detector called the cloud chamber, the path is made visible by condensing water droplets.

Notice that although the difference between the masses of two isotopes is very small, this arrangement helps us convert that small difference into an easily measurable separation distance. This arrangement is known as a mass spectrometer. A mass spectrometer is used in many fields of science, especially medicine, rocket science, geology, etc. In medicine, for example, anesthesiologists use it to measure respiratory gases, and biologists use it to determine reaction mechanisms in photosynthesis.

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The motion for the Charged Particle Under a Crossed Electric and Magnetic Field (Velocity Selector

Consider an experimental setup to illustrate the velocity selector. In the region of space in between the parallel plates of a capacitor producing a uniform electric field E, a uniform magnetic field B is maintained perpendicular to the direction of the electric field.

Suppose a charged particle with charge q enters  space from the left  with  velocity  v. The net force on the particle is     

For a positive one, Charge the electric force; the force on the charge acts downwards, while the Lorentz force acts upwards if these two forces are in balance.

That means the forces only act on the particle moving at a certain speed for a given size of fields E and B. This speed is independent of mass and charge.

The particle can be selected with a certain speed by the appropriate choice of electric and magnetic fields. Such an arrangement for fields is called a rate selector.

cyclotron

A cyclotron will be the device used to accelerate charged particles to high kinetic energy. It is also called a high-energy accelerator. Lawrence and Livingston invented it in 1934.

Principle

When a charged particle moves perpendicular to the magnetic field, it experiences the Lorentz magnetic force.

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Structure

The schematic diagram of a cyclotron. Particles can move between two semi-circular metal containers called Dees (hollow D-shaped objects). They are enclosed in a vacuum chamber and held in an area with a uniform magnetic field controlled by an electromagnet. The direction of the magnetic field is perpendicular to the plane. The two of them are separated by a gap, and the source S (which ejects the particle to be accelerated) will place between them in the middle of the gap. They are connected to a high-frequency alternating potential difference.

Work

Suppose the ion ejected from source S has a positive charge. Once the ion is ejected, it accelerates, which is a negative potential at that moment. Since the magnetic field is perpendicular to the plane, the ion moves in a circular orbit. After a semi-circular trajectory, the ion reaches space. At this point, the polarities are reversed, so the ion is now accelerating at a greater speed. The Lorentz force provides the centripetal force on the charged particle q.

The radius of the circular path increases with increasing speed. This process continues, and thus the particle moves in a spiral path with an increasing radius. As soon as it gets close to the edge, it is pushed out with the help of the deflection plate and can reach the target T.

The important condition for the cyclotron operation is that the frequency f of the positive ion that circulates in the magnetic field must be equal to the constant frequency of the electric oscillator. That is called the resonance condition.

From equation, we have 

The  period of oscillation is 

The kinetic energy for the charged particle is 

Limitations of the cyclotron

(a) Ion velocity is limited

(b) Electron cannot be accelerated

(c) Uncharged particles can’t be accelerated

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Force on a current-carrying conductor placed in a magnetic field

When a current-carrying conductor is placed in a magnetic field, the force acting on the conductor is equal to the sum of the Lorentz forces on the individual charge carriers in the conductor. Consider a small conductor segment of length dl with cross-sectional area A and current I. Free electrons move in the opposite direction to the current. Then the relationship between the current I and the magnitude of the drift velocity vd. 

(a) If the conductor is placed along the direction of the magnetic field, the angle is θ = 0. Hence the force experienced by the driver is zero. (b) If the conductor is perpendicular to the magnetic field, the angle θ = 90. Hence the force experienced by the conductor is maximum, which is  

Fleming’s left-hand rule 

When a contemporary sporting conductor is positioned in a magnetic discipline, the course of the pressure is skilled through its miles given through Fleming’s Left Hand Rule.

Stretch out the forefinger, the centre finger and the thumb of the left hand such that they’re in 3 at the same time perpendicular directions. If the forefinger factors withinside the course of a magnetic discipline, the centre finger withinside the course of the electrical contemporary, then the thumb will factor withinside the course of the pressure skilled through the conductor. 

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Force among lengthy parallel contemporary sporting conductors 

Let lengthy, instantly parallel contemporary sporting conductors separated through a distance r will store in an air medium. Let I1 and I2 be the electrical currents passing through the conductors A and B in equal course (i.e. alongside z – course), respectively. The magnetic internet discipline at a distance r because of contemporary I1 in a conductor.

From the thumb rule, the course of magnetic discipline is perpendicular to the aircraft of the paper and inwards, i.e. alongside the negative I course. 

Therefore, the pressure on dl of the twine B is directed toward conductor A. So the detail of duration dl in B is attracted in the direction of conductor A. Hence the pressure is in keeping with a unit duration of conductor B because of the contemporary withinside the conductor.

Similarly, the internal magnetic induction because of contemporary (in conductor B) at a distance r withinside the elemental duration dl of a conductor.

From the thumb rule, the course of magnetic discipline is perpendicular to the aircraft of the paper and outwards (arrow out of the page ), i.e., alongside the positive I course.

Therefore the pressure on the dl of conductor A is directed in the direction of conductor B. So the duration dl is attracted in the direction of the conductor.

Therefore, the force between two parallel current-carrying conductors is attractive if they carry current in the same direction.

The force between two parallel current-carrying conductors is repulsive if they carry current in opposite directions.

• Definition of Ampere

An ampere will define as the constant current which, when flowing through each of two infinitely long parallel straight conductors held side by side in parallel for a distance of one metre in air or vacuum, results in that each conductor experiences a force of 2 × 10-7  Newtons per metre of conductor length.

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TORQUE IN A CURRENT LOOP

The force on a current-carrying wire in a magnetic field is responsible for motor operation.

Torque in a current loop  in a magnetic field

Imagine a rectangular loop PQRS carrying current I and placed in a uniform magnetic field  B. Let an as well as b be the length and width of the rectangular loop, respectively. The unit vector nˆperpendicular to the loop plane forms an angle θ with the magnetic field. The force’s direction will be found using the right corkscrew rule, and its direction is upwards.

Since the forces FQR and FSP are equal, opposite and collinear, they cancel each other out. But the forces FPQ and FRS, which are equal in magnitude and directed in opposite directions, do not act along the same line. Therefore, FPQ and FRS form a pair that applies torque to the loop. The torque is acting on arm PQ about AB.

The torque acting on the arm RS is AB and points in the same direction. The total torque was acting on the entire loop about an axis AB along AB direction in vector form.

The torque tends to rotate the loop to align its normal vector with the direction of the magnetic field.

If there are N turns in the rectangular loop, then the torque is given by τ = NIABsinq Special cases:

(a) If θ = 90°, the plane of the loop is parallel to the magnetic field, and the torque in the current loop is maximum.  

(b) When θ = 0°/180° or the plane of the loop is perpendicular to the magnetic field, the torque in the current loop is zero.

Moving Coil Galvanometer: The moving coil galvanometer is a device used to measure the current flow in an electrical circuit.

Principle

A current-carrying loop is placed in a homogeneous magnetic field and experiences a torque.

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Construction

A moving-coil galvanometer consists of a rectangular PQRS coil of thin, insulated copper wire. The coil contains many turns wound on a light alloy frame. A cylindrical soft iron core is placed symmetrically inside the coil. The rectangular coil hangs freely between two pole pieces of a horseshoe magnet.

The upper end of the rectangular coil is attached to one end of a thin strip of phosphor bronze, as well as the lower end of the coil is connected to a helix also made of phosphor bronze. A small flat mirror is attached to a thin suspension strap to measure the coil’s deflection with the help of a lamp and a ruler. The other end for the mirror is connected to a torque head. To pass electrical current through the galvanometer, the suspension bracket and S spring are connected to terminals.

Working 

Consider a single turn for the rectangular coil PQRS whose length is l and width is b.   and. Let I be the electric current passing through the rectangular coil PQRS. The horseshoe magnet has hemispherical magnetic poles that create a radial magnetic field. Because of this radial field, sides QR and SP are always parallel to magnetic field B and experience no force. Sides PQ and RS are always perpendicular to the magnetic field and experience equal forces in opposite directions. This creates torque.

For a single turn, the bending moment is in the coil area.

The torque diversion twists the spool and develops a self-aligning torque (also called a self-aligning torque). Therefore, the moment of the restoring pair is proportional to the magnitude of the torque θ.

K is the restoring torque per unit torque.

In equilibrium, the deflection torque must be equal to the restoring torque. GKNABI is called the galvanometer constant or galvanometer current derating factor.

Since the levitation coil galvanometer is very sensitive, we must be careful when performing the experiments. Most of the galvanometers we use are pointer-type moving coil galvanometers.

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Galvanometer Figure of Merit

It is the current required to produce a one-division deviation in the galvanometer.

Sensitivity of a Galvanometer

The galvanometer is sensitive when it shows a large deflection even with a small current flowing through it or a small voltage applied across it.

Current sensitivity is defined as the deflection produced per unit of current flowing through the galvanometer.

The current sensitivity of a galvanometer can be increased by:

(i) by increasing the number of turns, N

(ii) by increasing the magnetic induction, B

(iii) increasing the coil area, A

(iv) Reduction of the torque per unit of the suspension wire, K.

Phosphor: Bronze wire is used as the suspension wire because the torque per unit is very small.

Strain Sensitivity

It will be defined as the displacement produced per unit strain applied across the galvanometer. Rg is the resistance of the galvanometer.

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Conversion of galvanometers into ammeters and voltmeters

A galvanometer is a very sensitive instrument for measuring current. It could be easily converted into an ammeter and voltmeter.

Galvanometer to an Ammeter 

An ammeter is a tool to grade cutting-edge flowing within the electric circuit. The ammeter should provide low resistance such that it’ll now no longer extrude the cutting-edge passing via it. So the ammeter is hooked up in the collection to degree the circuit cutting-edge. A galvanometer is transformed into an ammeter by connecting a low resistance parallel to the galvanometer. This low resistance is known as shunt resistance S. The scale is now calibrated in Ampere, and the variety of ammeter relies upon the shunt resistance values. 

Let me be the cutting-edge passing via the circuit. When cutting-edge I reach junction A, it divides into components. Let It pass via the galvanometer of resistance R g via a direction AGE, and the last cutting-edge (I – Ig ) pass alongside the direction via shunt resistance S. The fee of shunt resistance is so adjusted that cutting-edge I produces complete scale deflection withinside the galvanometer. The capability distinction throughout the galvanometer is identical because the capability distinction is throughout shunt resistance.

The deflection withinside the galvanometer is proportional to the cutting-edge passing via it. 

The deflection produced withinside the galvanometer is a degree of the cutting-edge I passing via the circuit. 

Shunt resistance is hooked up in parallel to the galvanometer. Therefore, the resistance of the ammeter may be decided through computing the powerful resistance.

Since the shunt resistance is totally low resistance and the ratio is likewise small. This means the resistance presented through the ammeter is small. So, whilst we join the ammeter in the collection, the ammeter will no longer extrude drastically the cutting-edge within the circuit. For a perfect ammeter, the resistance should be the same as 0. But in reality, the studying in the ammeter is constantly much less than the real cutting-edge withinside the circuit. Let me be the cutting-edge measured through the best ammeter, and I will be the real cutting-edge withinside the circuit. Then, they share mistakes in measuring a cutting-edge via an ammeter.

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Key points

1. An ammeter is a low resistance tool whose miles are constantly related in a collection to the circuit.
2. The best ammeter has 0 resistance.
3. To boom the variety of ammeter n times, the fee of shunt resistance is related in parallel.

Galvanometer to Voltmeter

A voltmeter will be the instrument used to measure the potential difference between any two points in electrical circuits. It must not draw current from the circuit; otherwise, the value of the potential difference to be measured changes.

The voltmeter must have high resistance and, when connected in parallel, draws no appreciable current to show the true potential difference.

A galvanometer will be converted into a voltmeter by connecting a high-resistance R in series with a galvanometer. The scale is now calibrated in volts, and the range of the voltmeter is based on the values ​​of the series resistor Rh, i.e. the value of the resistor is adjusted so that the current I produces a full-scale deflection in the galvanometer.

Let R g be the resistance of the galvanometer and let I be the current with which the galvanometer generates the full deflection. Hence the galvanometer is connected in series with high resistance, and the current in the circuit is equal to the current through the galvanometer. 

Since the galvanometer and high resistance are connected in series, the total resistance or effective resistance in the circuit is the sum of their resistances. This gives the resistance of the voltmeter.

The galvanometer reading is proportional to the current. But the current is proportional to the potential difference. Therefore, the deflection in the galvanometer is a measure of the potential difference. Because the resistance of the voltmeter is very large, a voltmeter connected in parallel in a circuit will draw less current into the circuit. An ideal voltmeter has infinite resistance.

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Key points

1. The voltmeter is a high-impedance instrument and is always connected in parallel with the circuit element at which the potential difference is measured.
2. An ideal voltmeter has infinite resistance.
3. To increase the range of the voltmeter by n times the  resistance value, it must be placed in series with the galvanometer

SUMMARY 

• A vertical plane that runs through a geographic axis is called a geographic meridian.
• A vertical plane passing through the magnetic axis is called the magnetic meridian.
• The magnetic meridian’s angle at a point with the geographic meridian is called the declination of magnetic declination.
• The angle the Earth’s total magnetic field  B makes with the horizontal direction at the magnetic meridian is known as the magnetic tilt or tilt at the given point.
• The magnetic moment is the product of its pole strength and magnetic length. It is a vector quantity denoted by  pm.
• The magnetic field is the region surrounding a magnet where the magnetic pole of unity forces experiences a force. It is a vector quantity and is denoted by  B.
• The number of magnetic field lines that normally cross the given area is called the magnetic flux ΦB. It’s a scalar quantity. In the SI unit, the magnetic flux ΦB is denoted by Weber with the symbol Wb.
• Coulomb’s law statement in magnetism  states clearly: “The attraction or repulsion force between two magnetic poles is proportional to the product of the forces of their poles and inversely proportional to the square of the distance between them.”
• The magnetic dipole, remaining in the uniform magnetic field, experiences a torque. The
• A tangent Galvanometer is a device for measuring very small currents. It is an example of a moving magnet-type galvanometer. Its operation depends on the tangent law.
• The tangent law reads B = BH tan θ.
• The magnetic field magnetising the specimen or sample is known as the magnetising field. It is a vector quantity denoted by  H, and its unit is A m–1. The measure of a material’s ability to transmit lines of magnetic force is called magnetic permeability.
• The net magnetic moment per unit of material is called the magnetisation intensity.
• The magnetic susceptibility is the ratio of the magnetisation strength induced by the magnetisation field H in the material.
• Magnetic materials can be divided into diamagnetic, paramagnetic, and ferromagnetic materials.
• The lag of the magnetic induction  B versus the cyclic change of the given magnetising field  H is called “hysteresis”, which means “lag”.The right-hand rule of thumb states: “Assuming we are holding the current-carrying wire in the right hand with the thumb pointing in the direction of the current flow,  the remaining fingers surrounding the wire point in the opposite direction from the magnetic field lines. Produced”.
• Maxwell’s right corkscrew rule states: “If we turn a screw with a screwdriver, then the current direction is the same as the direction in which the screw moves and the direction of rotation of the screw determines the direction of the screw” of the magnetic field”.
• The magnetic field inside the coil is given by, where n is the number of turns per unit length.
• The magnetic field inside the toroid is given by, where n is the number of turns per unit length.
• The charged particle moving into the uniform magnetic field would experience a circular motion.
• Fleming’s rule for the left-hand states: “Stretch the index finger, middle finger, and thumb of the left hand so that they are in mutually perpendicular directions. If we hold the index finger in the direction of the magnetic field, the finger is medium in the direction of the magnetic field. Electric current, then the thumb points in the direction of the force exerted on the conductors. When the coil is brought into the uniform magnetic field, its net force is always zero, but the net torque is not zero. The magnitude of the net torque is τ = NABI sin θ.
• A moving Coil Galvanometer is an instrument used to detect and measure small currents.
• In the moving-coil galvanometer, the current through the galvanometer is directly proportional to its displacement. Mathematically I = Gθ, here G is called galvanometer constant or current reduction factor.
• Current sensitivity means the deviation that occurs per unit of current flowing through it. Voltage sensitivity means the displacement that occurs per unit of a voltage applied across it. Rg is the resistance of the galvanometer.
• An ammeter is an instrument used to measure the current in the circuit.
• A galvanometer could be converted into an ammeter of a given range by connecting it to a suitable low impedance S, known as a shunt, in parallel with the given galvanometer.
• An ideal ammeter has no resistance. The
• voltmeter is used to measure each circuit element’s potential difference.
• A galvanometer could be made a suitable voltmeter of a particular range by connecting it with a suitably high resistance Rh in series with the particular galvanometer.
• An ideal voltmeter has infinite resistance.

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Class 12 Physics Chapter 5 notes: Exercise & Answer Solutions

One can find all the NCERT solutions to the exercises covered in the chapter in the Class 12 Physics Chapter 5 notes and ensure success in their examinations.

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