CBSE Class 12 Physics Revision Notes Chapter 1

Class 12 Physics Chapter 1 Notes – Electric Charges and Fields Notes

Physics is a very important subject in the life of every science student who wants to do well and get a good score. Science students, whether they are interested in pursuing medical, engineering or of the other science fields, will need to study and develop clear concepts in Physics and score well in the examination. While Class 12 Physics is no doubt a tough subject, Extramarks subject matter experts have curated study material to make it easier for students to study, understand concepts, and score well. 

Extramarks Class 12 Physics Chapter 1 notes are important subject material for preparing for exams.It will help students revise accurately and correctly in the least amount of time possible and better understand the concepts. This topic is more important in board exams and competitive entrance exams.The topic of electric charges and fields is explained very well in the Class 12 Physics Chapter 1 Notes, and this study material can assist you in understanding this subject better.

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Key Topics Covered in Class 12 Physics Chapter 1 Notes

Class 12 Physics Chapter 1 Notes is all about Electric Charges Class 12 Physics Chapter 1 Notes and Fields. It is a fundamental topic in Physics.

The electric charge, its properties, and the electric field are all covered in this chapter. Electric charge is the physical attribute of matter that causes other matter to experience a force in the electromagnetic field. In Class 12 Physics Chapter 1 notes, numerous equations and rules are discussed based on Electric Charge and Electric Field.

Electric Charges and Fields, Class 12 Physics Chapter 1 notes, provides a foundation for practical application questions and a proper explanation of these equations and principles.

Students will come across several fundamentals themes when they read the CBSE Class 12 Physics Chapter 1 Notes, such as

• Charged with electricity
• The potential energy of electricity
• The electric fields and possible relationship
• Dipoles made of electricity
• The implementation of Gauss’s Law
• The characteristics of a conductor
• Theory of plates
• Charge Characteristics
• Electroscope
• The Law of Coulomb
• Potential Energy of Electricity

While these Class 12 Physics Chapter 1 notes are very helpful, simply reading them will not suffice; you must practise the Class 12 Physics Chapter 1 notes as well as all other Extramarks that study material content and apply theoretical principles to reality to better understand the concepts.

Electric Charge

Electric charge is the basic property of matter, and it gets carried by some elementary particles that govern how the particles are affected when present in an electric or magnetic field. Both positive and negative electric charges occur in discrete natural units, and they cannot be created nor destroyed.Types

Electric charges are of two general types:

Positive and Negative.

Two objects with an excess of the same type of charge repel each other when they are relatively close together. Two objects with opposite charges attract each other when relatively nearby.

 Unit and Dimensional Formula

The S.I. unit of charge is the coulomb (C),

(1mC=10−3C,1μC=10−6C, lnC=10−9C)(1mC=10−3C,1μC=10−6C,ln⁡C=10−9C)

C.G.S. The unit of charge is e.s.u. 1C=3×1091C=3×109 esu

The Dimensional formula is given by [Q]=[AT][Q]=[AT].

 Properties of Charge

There are three basic properties of an electric charge:

Quantisation- As per this property, the total charge of a body is an integral multiple of the basic charge  

Additive- This electric charge property reflects an overall body charge as the algebraic sum of all individual charges acting on the system.

Conservation- According to the laws of conservation, the total charge of a system remains constant throughout time. In other words, when objects become charged because of friction, the charge is transferred from one object to another. There is no way to create or eliminate charges.

Point Charge

An electric charge is a point charge. When liner sized charged bodies are placed nearby, and the sizes of the charged bodies are much smaller compared to the distance between them, their linear sizes can be ignored, and the charged bodies are referred to as point charges.

Comparison of Charge and Mass

Basis for Comparison	Charge	Mass
Basic	It produces electric fields.	It produces a gravitational field.
Classification	Positive and negative	Always positive
Denoted as	q	m
Nature	Quantised	Non-quantized
SI unit	Coulombs	Grams or Kilograms
Existing force	Attractive or repulsive	Attractive only
Conservation	Exist	Not exist
Dependency on speed	Independent	Dependent
Existence	Cannot exist without mass	Can exist without charge

Methods of Charging

(1) Friction: When two bodies rub against each other, electrons are transferred from one to the other.

As a result of this electron transfer,  one of the bodies gets an excess of positive charge, while the other gets an excess of negative charge.While rubbing a glass rod with silk, the glass rod becomes positively charged while the silk becomes negatively charged.

However, when rubbing ebonite with wool, the ebonite becomes negatively charged, while the wool becomes positively charged.

Friction causes clouds to get charged as well.

Due to the passage of electrons between the two bodies, both positive and negative charges in equal amounts arise simultaneously during charging by friction due to the conservation of charge.

(2) Electrostatic induction: When a charged body is brought close to an uncharged body, the charged body attracts the opposing charge and repels the same charge in the uncharged body.

As a result, one side of the neutral body (near the charged body) becomes inversely charged while the other remains neutral.

This is known as electrostatic induction.

The charge of the inducting body does not increase or decrease.

The highest value of the induced charge is given by Q’=-Qleft[1-frac1K rt], where Q is the inducing charge and K is the dielectric constant of the substance of the uncharged body. The dielectric constants of various media are listed in the table below.

Medium	K
Vacuum/air Water Mica Glass Metal	1 80 6 5–10 ¥

The dielectric constant of an insulator can not be

For metals in electrostatics and so, i.e. in metals, the magnitude of the induced charge is equal and opposite to the inducing charge.

(3) Conduction charging:

Consider two conductors, one charged and the other not. Assure that the conductors are in contact with one another.

The charge will spread along both conductors due to its repulsion. As a result, all conductors will be assigned the same sign.

This is known as charging via conduction (using contact).

Electroscope : 

It’s a device that detects the existence and amount of an electrical charge. The leaf inside the electroscope repels or attracts the charged body when the instrument’s top is brought near it, depending on the charge of the body placed near it.

If the body is negatively charged, electrons from the top of the electroscope are pushed downward, causing the two leaves to repel one another.

If the body is positively charged, electrons from the electroscope’s top are pushed upward, attracting the two leaves together.

Coulomb’s Law:

The attractive force of repulsion between any two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of their distance between them, according to Coulomb’s law.This attractive force acts on the line connecting the two charges, called point charges.

Coulomb’s Law can be put down as follows:

Where k is the proportionality constant.

In SI units, k has the value,

(a) The force is always directed along the line connecting the two charges.

(b) If the charges are of the same sign, they will experience repulsive force; if they are of opposite signs, the force is attracting.

(c) The nature of this force is conservative.

(d) It’s also known as the inverse square law. 

Variation of K: 

The unit system and the medium determine the constant k between the two charges.

In C.G.S. for air

In S.I. for air

Effect of Medium:

The effect of the medium (a) When a dielectric medium is filled in between charges, the charges inside the dielectric medium rearrange, and the force between the same two charges decreases by a factor of K, also known as the dielectric constant; K is also known as the medium’s relative permittivity r.

Therefore, in the presence of a medium.

Medium	K
Vacuum/air	1
Water	80
Metal
Glass	5-10
Mica	6

Principal of Superposition:

According to the concept of superposition, the total force acting on a particular charge due to several charges is the vector sum of the individual forces acting on that charge due to all the charges.

Consider a number of charges Q1, Q2, Q3…..are applying force on a charge Q

 The net force on Q will be

Fnet = F1 +F2 +F3 +……..+ Fn

The magnitude of the final two electric forces is given by,

F = F12 + F22 + 2F1F2cosϴ

The force direction is given by,

Tan ⍺ = F2 sinϴF1  + F2 cosϴ

Electric Field:

It is stated that a positive or negative charge creates a field around itself. An electrical field is a region around a charge in which another charged particle perceives a force. 

Electric Field Intensity: 

The force that is experienced by a positive unit charge placed at any point determines the electric field intensity.

E = F/qo 

Where q00 denotes that the existence of this charge does not affect the source charge Q’s electric field, hence the formula for electric field intensity can be written as 

E = qo0F/qo

Unit and Dimensional formula: Its S.I. unit is,

[E] = [M L T-2 A-1 ]

The direction of the electric field: Field of electricity (intensity), the amount E is a vector quantity.

A positive charge’s electric field is always away, while a negative charge’s field is always toward the charge. 

Electric Force and Electric Field Relationship:

A charge (Q) experiences a force F=QE in an electric field \vec E.

If the charge is positive, force is directed in the field’s direction; if the charge is negative, force is directed in the opposite direction.

Superposition of Electric Field

The vector sum of electric fields attributable to multiple charges at any place equals the resultant electric field. 

E = E1 +E2 +E3 +……..+ En 

The formula can be used to calculate the magnitude of the resultant of two electric fields.

E = E12 + E22 + 2E1E2cosϴ

Point Charge

The electric field of a point charge is generated at a point P r away from it and is given by,Ep = Q4r2

Continuous Charge Distributions

There are an infinite number of ways in which we can spread a continuous charge distribution over a region of space. Mainly, three types of charge distributions will be used. We define three different charge densities.

Symbol	Definition	S I Units
(lambda)	Charge per unit length	C/m
(Sigma)	Charge per unit area	C/m2
(rho)	Charge per unit volume	C/m3

We can calculate charge densities if a total charge q is distributed along a line of length ℓ, over a surface area A or throughout a volume V.

= q/l

= q/A

= q/V

Electric Field Line Properties:

1. An electric field line starts with a positive charge and ends with a negative charge.
2. The magnitude of a charge is proportional to the number of field lines originating/terminating on it.
3. The magnitude of the Electric Field will be proportional to the number of Field Lines travelling through the perpendicular unit area.
4. The direction of the Electric Field at any place is determined by being tangent to a Field line. If the charge is held there, this is the path it will take in an instant.
5. There can never be a point where two or more field lines cross.

(They can’t have more than one direction)

6. Uniform field lines are straight, parallel, and evenly spaced.
7. There is no way to make a loop with field lines.
8. Electric field lines start perpendicular to the conductor’s surface and end perpendicular to the conductor’s surface. Inside a conductor, there are no electric field lines.
9. Field lines are always oriented from higher to lower potential.

There will be no field lines if there is no electric field in a region.

The motion of a charged particle in an electric field:

(a) When a charged particle is placed in a uniform field when it is originally at rest:

Place a charged particle with mass m and charge Q at rest in an electric field of strength E.

F = QE

(i) Acceleration and force:

F=QE is the force that the charged particle is subjected to. Positive charges are pushed towards the electric field, whereas negative charges are pushed in the opposite direction.

a = F/m 

a = QE/M

This force produces an acceleration of a=Fm=QEm.

Since the field E is constant, the acceleration is constant. Thus, the motion of the particle is uniformly accelerated.

(ii) Velocity:

Assume that at point A, aparticle is at rest and travels to point B in time t.

V= potential difference between A and B.

S= Separation between A and B.

By using the equation,

v = u + at

v = 0 + QE/m

(iii) Momentum:

Momentum p=mv

p = QEt

(iv) Kinetic energy:

In time t kinetic energy gained by the particle is,

K = 12mv2 = Q2E2t22m

(b) When a charged particle enters at a right angle to the uniform field’s starting velocity.

When a charged particle enters an electric field perpendicularly, it follows a parabolic path, as depicted.

(i) Trajectory Equation: 

A particle moves with a constant velocity along the x-axis, and the equation x=ut gives the horizontal displacement(x).

We’ll use the equation of motion for uniform acceleration to get displacement y because the particle’s motion is accelerated along the y-axis.

S = ut + ½ at2

Along the y-axis, u=0,

Hence s = ½ at2

And for displacement along the x-axis, t = x/u

From the above equations, it can be said that y ∝ x2

(ii) Velocity at any instant: 

T vx = u 

Vy = QEt/m

So, 

V = u2 + Q2E2t2M2

Potential Energy of Electricity:

The potential energy is defined as the energy required to move a charge in the presence of an electric field.To move a charge deeper in the electric field, you’ll need more energy, but you’ll also need more energy to move it through a stronger electric field.

Potential Energy of a System with Two Charges:

Change in potential energy is always designed as- ΔU=−Wconservative force =−Wcoloumb force

A system of charges in a specific configuration is defined by its potential energy.

Consider a two-charge system, q1 and q2. Assume that the charge q1 is constant and that the charge q2 is transferred from point A to point B.

The electric force on charge q2 is F = q₁q₂4 ₀r² r    

As the charge moves from B to C, the total work done is W=     r1     r2q₁q₂4 ₀r²dr = q₁q₂4 ₀1r1–1r2     

Change in potential energy Ur2 − Ur1 = − W = q1q24 ₀1r1–1r2    

When the two-charge system has infinite separation, the potential energy of this two-charge system is assumed to be zero.

When the spacing is r, the potential energy is

 U =r − Ur −  U = q1q24 ₀1r1–1   = q1q24 ₀r

The potential energy is mostly determined by the distance between the charges and is unaffected by the charged particles’ spatial location.

 The electric potential energy possessed by a pair of charges is calculated using the above equation.

Electron Volt (eV):

In atomic and nuclear Physics, it is the smallest functional unit of energy. The energy gained by a particle with one quantum of charge one e when accelerated by 1 volt is defined as “the energy acquired by a particle containing one quantum of charge one e when accelerated by 1 volt i.e.

1eV = 1.6 10-19C 1JC = 1.6 10-19J = 1.6 10-12erg

Potential Energy of an n-Charged System

In a system with n charges, the electric potential energy for each pair is computed, and then all of the energies are summed algebraically. i.e.,

U = 14 ₀Q1 Q2r12+Q2 Q3r23+………….. and in case of a continuous distribution of charge.

As dU = dQ⋅V ⇒ U = ∫ VdQ

, e.g., Electric potential energy for a system of three charges:

Potential energy = 14 ₀Q1 Q2r12+Q2 Q3r23+Q3 Q1r31

Electric Potential:

Assume that a test charge q is transported from point A to point B in an electric field while all other charges in the system remain stationary. We define the potential difference between point A and point B as UB-UA if the electric potential energy changes by UB-UA due to this displacement.

\Delta V = \Delta Uq i.e., vB− vA = UB – UAq = Wextq \Delta KE=0

Conversely, if a charge q is taken through a potential difference 

vB− vA , the electric potential energy is increased by U.B. – U.A. =  qvB– V.A.

Also Wext = qvB– v KE=0

The potential difference between the two points indicates the amount of work required to move a charge between them.

 Electric Potential Due to a Point Charge:

Consider the case of a point charge Q at point A. The  potential at P is,

Vp −  V = Up – Uq = Q4 ₀r Vp = Q4 ₀I

 ∵Vis taken as 0

Finding the electric potential due to a system of charges using equations and then putting them together yields the electric potential due to a system of charges. Thus,

V = 14 ₀ Qiri

Since the electric potential is a scalar variable, the sign of charges used in the expression is V.

Unit and Dimensional Formula:

S.I. unit − JouleCoulomb = volt

V = ML2T-3A-1

Types of Electric Potential:

Charge potentials are classified into two types based on their nature.Because of the positive charge, there is a positive potential.

Because of the negative charge, there is a negative potential.

Note:

• V=0 but E0 in the middle of two equal and opposite charges.
• At the intersection of two lines of equal and identical charge V0,E=0.
• If given the freedom to move,

Positive charge moves indefinitely from higher to lower potential points.A negative charge moves from lower to higher potential points at all times.

(Because this motion reduces a system’s potential energy.)

 Relation Between Electric Field & Potential:

A potential gradient is the rate of change of an electric field with distance.It’s a vector quantity with the opposite direction of the electric field. The relationship between the potential gradient and an electric field is E=-dVdr; this equation yields another unit of the electric field, the voltmeter. The negative sign in the above relationship implies that the electric field potential decreases in the direction of the electric field.

We can also write in the space around a charge distribution,

E = EZi + Eyj + Ezk

where EX = − dVdX,Ey = − dVdy and  Ez=- dVdz

The potential difference between points A and B is,

vB− vA = −  A    BE . dr

Since displacement is in the direction of the electric field, hence θ = 00

so, vB− VA = −  A    BE . dr cos0 =   A    BE . dr = − Ed

Electric Dipole:

General Information:

A dipole is a system of two equal and opposite charges separated by a tiny, constant distance.

(i) Dipole axis: A dipole’s axis is the line that connects its negative and positive charges. It’s also known as the longitudinal axis. 

(ii) Equatorial axis: The dipole’s equatorial or transverse axis, perpendicular to the length, is called its equatorial or transverse axis.

(iii) The distance between two charges is called the dipole length (d).

(iv) The dipole moment is a quantity that indicates the strength of a dipole. It is a vector quantity directed along the axis from negative to positive charge. It is symbolised by the letter p and defined as the product of  two numbers.

I.e, P = qd

It’s S.I. The unit is the coulomb-metre or Debye 1 Debye = 3.3 × 10-30C × m and its dimensions are  M0L1T1A1.

Note:

1. Only an electric field exists in the area surrounding a stationary electric dipole.
2. When an electric field is applied to a dielectric, its atoms or molecules become small dipoles.

Electric Dipole in a Uniform Electric Field:

Force and Torque: When a dipole is placed within a uniform field such that the dipole (i.e., p) makes an angle with the field direction, two equal and opposite forces are acting on the dipole from a couple whose tendency is to rotate the dipole, resulting in torque, and the dipole attempts to align itself in the field direction. Consider an electric dipole in a homogeneous electric field, with the dipole (i.e., p) forming an angle  with the electric field direction as illustrated.

(a) Electric dipole net force  Fnet=0.

(b)  ………. = pEsinθ =p × E

(ii) Work: It is evident from the preceding explanation that a dipole in a homogeneous electric field seeks to align itself in the direction of the electric field (i.e., equilibrium position). It will take some effort to adjust its angular position.

If an electric dipole is held in a uniform electric field by creating an angle of 1 with the field and then turned to make an angle of 2 With the field, the work done in this operation is given by the formula.

W  =  qE cos\theta1 – cos/theta2

(iii) Potential energy of a dipole (in a uniform field) is defined as the work done in rotating it from a perpendicular to the field to the specified direction, i.e. if 1=90 degrees and 2= then

W = 𝛿U = U – U900  = –PEcos

U = – PEcos∵U900 = 0 or U =-PE

Neutral Point:

The resultant electric field at a neutral point is zero. As a result, neutral points can only be found where the resultant field is subtractive.

(a) At a position along the line connecting two like charges (due to a two-point charge system): Assume the two are similar. As indicated in the following diagram, Q1 and Q2 are separated by a distance x along a line.

If N is the neutral point at a distance of x1 from Q1 and x2(=x-x1) from Q2, then the natural point at N is,

E.F. due to Q1 = E.F due to Q2 i.e.,

14 ₀ . Q1x12 = 14 ₀ . Q2x22 Q1Q2 = x1x22

Note:

The neutral point is at the centre of the above calculation if Q1=Q2; remember that the resultant field at the middle of two equal and similar charges is zero.

(b) Due to a system of two unlike  charges at an external point along the line connecting two unlike charges:

Assume two opposite charges, Q1 and Q2, are separated by a distance x.

The neutral point is located outside the line connecting two opposed charges and is also closer to the charge that is lower in magnitude.

If |Q1|<|Q2, then the neutral point will be found on the side of Q1, assuming it is at a distance of l from Q1.

Therefore, at the point of neutrality,

KQ1l2 = KQ2x + l2  Q1Q2 = x + 22

Short trick: ℓ = xQ2/Q1 – 1

Note:

 The neutral point will be infinity if the above equation|Q1|=|Q2|.

Equilibrium of Charge:

(a) Definition: If the net force exerted on a charge is zero, it is said to be in equilibrium. A system of charges is considered to be in  equilibrium only if each charge is in equilibrium.

(b) Types of equilibrium: There are three types of equilibrium:

(i) Stable equilibrium: If a charged particle is displaced from its equilibrium location and subsequently returns, it is in stable equilibrium. If U is the potential energy, then U is the smallest in a stable equilibrium.

(ii) Unstable equilibrium: A charged particle is said to be unstable if it never returns to its equilibrium location after being displaced from it. In unstable equilibrium, U is maximal.

(iii) Neutral equilibrium: When a charged particle is displaced from its equilibrium position, if it does not return or move away but remains in the same location, it is considered to be in a neutral equilibrium, and U is constant in neutral equilibrium.

1. c) Charge balance in various situations

Assume three charges are comparable. As demonstrated here, Q1,q, and Q2 are aligned straight.

Case 1:

Charge q will be in equilibrium if F1 = F2 ie.,,Q1Q2 = X1X22

This is the charge q equilibrium condition. We can state that charge q is stable and that this system is not in equilibrium after following the instructions.

x1 = x1 + Q2/Q1 and x2 = x1 + Q1/Q2

e.g. if a distance of 30cm separates two charges +4μC and +16μC from each other, then for equilibrium, a third charge should be placed between them at a distance

X1 = 301 + 16/4 = 10 cm or X2 = 20 cm

Case 2:

Two charges that are similar As indicated below, Q1 and Q2 are positioned in a straight line at a distance of x from each other, with a third different charge, q, put in between them.

If |F1|=|F2|, charge g will be in equilibrium.

i.e., Q1Q2 =  X1X22

Note:

The same short trick can be used here to find the position of charge q as we discussed in Case-1, i.e.,

x1 = x1 + Q2/Q1 and x2 = x1 + Q1/Q2

It is critical to understand that the magnitude of charge q can be identified if one of the extreme charges (Q1. or Q2) is in equilibrium, i.e. if Q2 is in equilibrium, then the size of charge q can be determined.

q = Q1x2/x2, and if Q1 is in equilibrium, then q = Q2x2/x2 (It should be remembered that the sign of q is opposite to that of Q1 (or Q2))

Case 3:

Two dissimilar charges, Q1 and Q2, are placed along a straight line at a distance x from each other, a third charge, q, should be placed outside the line joining Q1 and Q2 for it to experience zero net force.

(Let |Q2|<∣Q1) 

Short Trick :

For its equilibrium. Charge q lies on the side of the charge that is smallest in magnitude, and

d= xQ1/Q2– 1

Time Period of Oscillation of a Charged Body:

T(a) Based on a basic pendulum: If a simple pendulum with length l and mass m oscillates about its mean position, the oscillation time is T=2l/g.

Case 1: If the bob is given a charge, say +Q, and an electric field E is applied in the direction depicted in the diagram, the charged bob’s equilibrium position (point charge) moves from O to O’.

On displacing the bob from its equilibrium position or

Or. It will oscillate under the effective acceleration ′g′, were

If the bob gets displaced from its equilibrium position O., it will oscillate at g′, which is the effective acceleration.

mg′= mg2+ QE2 g′ = g2+ QE/m2

Hence the new time period is T1 = 2lg’

T1 = 2 lg2 +QE/m12  

Since g′ > g, hence T1 < T

Case 2: If the electric field is applied downward, then 

Effective acceleration g′ = g + QE/m

So new time period T2 = 2ilg +QE/m

T2 < T1

Case 3: If the electric field is applied in an upward direction, then,

g′ = g − QE/m

So new time period T3 = 2ilg – QE/m

T3 > T

(b) Charged circular ring: A thin stationary ring of radius R has a positive charge of +Q unit.

Suppose a negative charge q (mass m) is positioned at a modest x distance from the centre. The particle’s motion will, after that, be simple harmonic motion.

At the -q charge site, there is an electric field.

E = 14 ₀ . Qxx2 + R232 

 Since x R, so x2 neglected hence E = 14 ₀, QxR3

Force experienced by charge −q is F = −q14 ₀, QxR3

F –x hence motion is simple harmonic

Having time period T = 24 ₀mR3Qq

(c) Spring mass system: As depicted, a mass m block holding a negative charge Q is placed on a horizontal, frictionless table and is attached to a wall by an unstretched spring of constant spring k. When electric field B is supplied, as depicted in the diagram, the block receives an electric force, which causes the spring to compress and the block to return to its original position. Under the influence of an electric field, this is known as the block’s equilibrium position. If the block is crushed or stretched more, it will oscillate with a time period of T=2m/k. Electric field =QE/k causes maximum compression in the spring.

Electric Potential Energy:

Consider n(n1)2 pairs of charges when expressing the total potential energy of a system with n charges.

Applying the Work-Energy Theorem:

Electric Potential

Potential Due to Charge Distribution:

Suppose we have volume charge density (ρ) and its position vector is a. Then, the entire charge distribution is integrated to calculate the electric potential at point P due to the continuous distribution of charges.

-EQ

A spherical shell with a uniform charge:

Outside the spherical shell, there is a point:

Because the point is outside the uniformly charged spherical shell and the radius exceeds R, the electric potential is

-E.Q.

As the shell is concentrated at its centre, the electric field outside a uniformly charged spherical shell is identical to the electric field created by the shell.

Point inside the spherical shell: 

Because this point is inside the spherical shell, the radius is smaller than R, and the electric potential is smaller.

-E.Q.

We have three alternative formulas for each charge distribution, similar to the electric field intensity.

Charge Distribution on the Line:

-E.Q.

, where is the charge density of the line.

Charge Distribution on the Surface:

-E.W.Q.

, where is the charge density on the surface.

Distribution of Volume Charges:

-E.Q.

Zero Potential resulting due to a System of Two Point Charge:

(i) At any finite point, the resultant potential is not 0 if both charges are equal.

(ii) If the charges are unequal and unlike, the curve is closed at all places where the resultant potential is zero.

(iii) There are two such sites along the line connecting the two charges, one inside and one outside, on the line connecting the charges. Both of the points mentioned earlier are closer to the lesser price.

For internal point:

Q1X1 = Q2X –X1 X1 XQ2/  Q1 + 1

For external points:

Q1 and Q2(opposite signs)Q1<Q2

Q1X2 = Q2X +X2 X2 = XQ2/  Q1 – 1

Electric Dipole:

A pair of objects with equal magnitude and opposite type of charges separated by a substantial distance is called an electric dipole. Consider two charges with the same magnitude ‘Q’ separated by a distance ‘D’. The first charge is assumed to be negative, while the second charge remains positive. This particular combination is known as an electric dipole. As a result, an electric dipole is generated when equal and opposing charges are grouped and separated by a certain distance.

Electric Field Due to a Dipole:

Using the concept that if we know the potential electric field can be calculated, we have already calculated

Vp = KP cosθr2

To Calculate the net electric field at P, we need E(Radial Component) & E1 (tangential component) of the electric field at P.

Er = -dvdr (When we travel in the radial direction).

Et = – dvrdθ (When we travel in the tangential direction).  

Vp = KP cosθr2

Er = -ddrkp cosθr2 = 2kp cosθr3

Et =–drdθkp cosθr2 = -kPr3 ddθ = kP sinθr3

Enet = Er2 +Et2 = kPr32  4cos2+sin2

Enet =kPr321+3cos2

Enet = kPr31+3cos2

tan = Et Er kPr3sinθ2kP cosθr3 = tanθ2 = tan-1tanθ2

(Note: is the angle with the radial direction)

Equilibrium of Dipole:

We know that the net torque as well as the net force experienced on a particle (or system) should be zero in any equilibrium.

When a dipole is placed in an electric field that is uniform, the net force is always zero. However, net torque will be zero only when the angle is equal to -E.Q.

When a dipole is situated parallel to the electric field, it is in stable equilibrium since, after turning it at asmall angle, the dipole strives to align itself in the direction of the electric field again.

It is considered to be in an unstable equilibrium when the dipole is placed opposite  the electric field.

𝜏 = 0   max   =pE  = 0

W = 0   W = pE             Wmax   =2pE

Umin=-pEU=0    Umax  =pE 

Angular S.H.M.:

If an electric dipole is slightly displaced from its stable equilibrium position in a uniform electric field (intensity E), it executes angular S.H.M. with a period of oscillation. If it is the dipole’s moment of inertia around the axis, through its centre and perpendicular to its length.

Electrified dipole: T=2I/pE

Dipole-Point Charge Interaction:

In a homogeneous electric field (intensity E), a dipole (electric) slightly moved from its stable equilibrium location executes angular S.H.M. with a period of oscillation if I is the moment of inertia of the dipole around the axis that passes through its centre and is perpendicular to its length.

Dipole that has been electrified  Fα1r3

Electric Dipole in a Non-Uniform Electric Field:

When an electric dipole is put in a non-uniform field, the two charges of the dipole are subjected to irregular forces, resulting in a net force on the dipole that is greater than zero.

A torque is created by two unequal forces acting on the dipole, causing it to rotate in the direction of the field.

In a non-uniform electric field, this is the case.

(i) The dipole’s motion is both translational and rotatory.

(ii) It may have no torque.

Gauss’s Law

Electric Flux-

Definition:

The electric flux is proportional to the count of field lines crossing or cutting any cross section in space. The size of the Electric Field will be proportional to the number of field lines going through the perpendicular unit area’ (Theory of Field Lines)

N.A.⊥ ∝ E N ∝ E

∴ Electric Flux, A = EA

Flux across area A decreases as rises. The area vector, A, corresponding to the area A, is defined as a vector of magnitude A drawn along the positive normal.

∴ Electric Flux, A = EA cosθ = E . A

Note: If the Electric field varies over the area of the cross-section, then

= A.E. dA

Unit and Dimension:

Flux is a scalar quantity.

Dimensional Formula: ML3T-3A-1

S.I. unit: (volt × m) or N.m2C

Types of Flux:

1) Electric Flux: An electric flux is the number of lines of the electric field that pass through a closed surface. E is the symbol for it.

2) Magnetic Flux: Magnetic flux represents the number of lines of the magnetic field that flow through a closed surface. M is the symbol for it.

Gauss’s Law:

Definition:

The total electric flux across a closed surface enclosing a charge is 10 times the magnitude of the charge

enclosed, according to Gauss’ Law.

i.e., not = 10Qcc

i.e., ∮ E.dA = QenE0

Note:

Gauss’s Law is valid only for a closed surface.

Gaussian Surface:

A Gaussian surface is a closed surface on which Gauss law can be applied.

Note:

1) Gaussian surfaces can be any shape or size; the only requirement is that they be closed.2) In nature, a Gaussian surface is hypothetical. It does not exist in the physical world.

Deriving Gauss’s Law from Coulomb’s Law:

Consider a spherical gaussian surface with the charge ‘+Q’ at its centre.

Field lines for a positive charge are usually radially outward, as we know.

E = kQr2 = Q4 ₀r2

Hence Net flux = Q/₀

Although the Gauss law was formulated for a spherical surface, it is true for any gaussian surface shape and any charge held anywhere inside the surface.

Coulomb’s Law from Gauss’s Law:

We’ll use an imaginary sphere (Gaussian surface) with a radius of r and a charge of +q as its centre. E must have the same magnitude at all places on the surface due to symmetry, and E points radially outward, parallel to dA. As a result, the integral in Gauss’s Law is written as:

net =  ∮ E.dA = ∮EdA = ∮dA = 4r2

Qenclosed = q

Thus, E4r2 = q₀ or Eq4 ₀r2

F = 14 ₀ qq0r2

Applications of Gauss’s Law:

Gauss’s Law is being used to derive ‘E’ from various charge distributions.

Electric Field Due to a Line Charge:

Consider an infinite line with a charge density that is linear. Let us calculate the electric field at a distance ‘r’ from the line charge using Gauss’s Law.

The cylindrical symmetry states that at a certain distance r from the line, the field strength will be the same at all places. If the charges are positive, this is the case. The field lines are perpendicular to the line charge and directed radially outwards.

A cylinder with a radius of r and a length of $textL$ is an adequate Gaussian surface. S2 and S3, E is perpendicular to dS on the flat end sides, implying that flux is zero. E . dS =EdS on the curved surface S1 because E is parallel to dS. Q=λL is the charge enclosed by the cylinder?

E∮ dS = E2πrL = L₀ or E = 2πε₀r = 2K r

Note:

At a distance r from the line, this is the field. If the charge is positive, it is directed away from the line; if the charge is negative, it is directed toward the line.

Uniform Spherical Charge Distribution:

P is a point outside the sphere at a distance r from the centre.

P = total chargetotal volume = Q43R3 = 3Q4R3

Outside the Sphere:

According to Gauss law  ∮ E.ds = Q₀ or E4R2 = Q₀

Eout = 14πε₀ . Qr2 and Vout= −    IEdr = 14πε₀ . Qr

using ρ = Q43R3

Eout = R33πε₀r2 and Vout= R33πJrV=0

Inside the Sphere:

The electric field inside the conducting charged sphere is zero, and the potential is constant everywhere and equals the surface potential. 

Graphical Variation of Electric Field and Potential With Distance

Uniform Spherical Volume Charge Distribution

We assume a spherical ,evenly charged distribution with radius R and total charge Q spread uniformly throughout the volume.

Density of charge

P = total chargetotal volume = Q43R3 = 3Q4R3

Outside the Sphere at P(r⩾R)P(r⩾R)P(r \geqslant R)

Gauss’ Law states that: -E.Q.

At the Surface of the Sphere

At surface r=R

Ee = 14πε₀. QR2 = ρR3πε₀ and Vs = 14πε₀. QR = R33₀

Inside the Sphere

At a radius of r from the centre. (r⩽R)

  ∮ Ein .  ds = qin₀ = Qr3₀R3 or Ejn4r2 = Qr3₀R3

Ein = 14πε₀ .Qr3R3 =r3₀Ein∝ rand

Vin = −  k  rE. dr = 14πε₀ Q3R2–r26a

Properties of Conductors

Inside a Conductor, Electrostatic Field Is Zero

Take a neutral or charged conductor, for example. An external electrostatic field could also be present. The electric field inside the conductor is zero in a static state.If the electric field is not zero, free-charge carriers will feel the force and drift. The free charges have dispersed so evenly in the static scenario that the electric field is zero throughout. Inside a conductor, the electrostatic field is nil.

At the Surface of a Charged Conductor, the Electrostatic Field Must Be Normal to the Surface at Every Point.

E would have a nonzero component along the surface if it weren’t normal to the surface. The free charges on the conductor’s surface would then be forced to shift. As a result, in a static scenario, E should have no tangential component. As a result, the electrostatic field at the surface of a charged conductor must always be normal to the surface. (Field is zero even at the surface of a conductor with no surface charge density.)

The Charge Kept in the Material of a Conductor Will Come to Its Outermost Surface.

We know that the electric field inside a conductor’s substance is zero at all times. This means that E′ is zero on the Gaussian surface at all places.

E.dA = Qe1₀ ⇒ E = 0 Qen = 0

Electrostatic Potential is Constant throughout the Conductor’s Volume and Has the Same Value (As Inside) on Its Surface.

This follows from results 1 and 2 above. Since E=0 inside the conductor has no tangential component on the surface, no work is done in moving a small test charge within and on its surface. That is, there is no potential difference between any two points inside or on the conductor’s surface. Hence, the result. If the conductor is charged, an electric field normal to the surface exists; this means the potential will be different for the surface and a point just outside the surface.

In a system of conductors of arbitrary size, shape, and charge configuration, each conductor is characterised by a constant value of potential. Still, this constant may differ from one conductor to the next

Electric Field on the Surface of a Charged Conductor

E = ₀n

where is a unit vector normal to the surface in the outward direction and is the surface charge density.

When the electric field is >0, it is normal to the surface outward; when it is >0, it is normal to the surface inward.

Gauss Law

Some Important Points About Gauss Law

1. The charge enclosed in the preceding phrase is (Q1 and Q2). Only Q1 and Q2 will have an impact on net flux.

On the other hand, the charge ‘E’ in the Gauss Law will be due to all of the charges Q1, Q2, Q3, and Q4. v

Qen=0

However, there is an electric field on the Gaussian surface.

3. If E is 0 at all places on the gaussian surface, then Qen must also be zero.

Because  ∮E dA =QenεD 

Zero Flux

When a surface encloses a dipole,

ɸ = 0; Qenc = 0

Inside a closed surface, the magnitudes of positive and negative charges are equal.

(ii) There are no charges.

The total flux associated with a closed body (without encapsulating any charge) placed in an electric field (either uniform or non-uniform) is zero.

Observe Flux through Common Geometrical Figures

Cube

(i) Charge at the centre of the cube.

Note:

ɸtotal = 1₀ :Q

Flux through each face, ɸface = Q6₀

We require eight cubes to enclose the charge at the corner in a Gaussian surface symmetrically—the total flux ϕT=Qε0. Therefore, the flux through one cube will be -E.Q. The cube has six faces, and flux linked with three faces (through A) is zero (ABCD, AHED, ABGH), so flux linked with the remaining three faces will

Now, as the remaining three are identical, so flux linked with each of the three faces will be -E.Q.

Hemisphere

ɸout = ɸin = R2E

ɸT = 0

ɸT = q₀, ɸhemisphere = q2₀

Cylinder

ɸT = q₀, ɸcy1 = q2₀

Cases of Earthing a Conductor

1. Charge distribution comes first, then earthing.

2. Assume some ‘x’ charge has flown to the ground following charge dispersal (after earthing).

3. Carry out a charge redistribution.

4. Measure the net potential of a location on the conductor (which is earthed) and compare it to zero. Determine the value of .

Vp = 0 = kQ1r2 + k–Q1r2 + kQ1+Q2-xr2 X = Q1 + Q2

A charge is flown from the outer surface because ‘-Q1’ will be induced on the inner shell as long as Q1 is there.

Vp = 0 =kQ1-xr1 + k–Q1-xr2 + kQ1+Q2-xr2

Q1-xr1 – Q1-xr2 + Q1+Q2-xr2 = 0

Q1r1 + Q2r2 = xr = x = Q1 + Q2r1r2

Note:

As can be observed, not all surface charge flows to the ground. The charge stored on the conductor’s outermost surface flows to the ground when the outermost conductor is earthed.

Connection of Charged Conductors

1. Before connecting, do a charge distribution.

2. Assume that a charge of ‘x’ is transferred from one conductor to another.

3. Charges should be redistributed.

4. Make the conductor’s net potential (1) equal to the conductor’s net potential (2).

Assumption: There is a significant distance between them.

Vp = VR kQ1-xr1 = kQ2+xr2 = Q1r2 –Q2 r1r1 + r2

Final Charges

Final common potential

This indicates that all the charges on shell (1) will flow to shell(2).

Self-Energy of Charged Sphere

Consider an evenly charged sphere with a total charge of Q and a radius of R. The labour done in getting the charges from infinity to build the sphere equals the electric potential energy of this sphere.

-E.Q.

Energy Density

Around a point in an electric field, the energy saved per unit volume is given by 

-E.Q.

Plate Theory

Charged Conducting Pate

-E.Q.

The net electric field at the point P, near a conducting surface, σ′ is given by [σ/ε0]

Parallel Plate Theory

To determine the charge distribution on each plate’s surface. Two conducting plates with area “A” (a large area in relation to distance, resulting in a uniform field) and thin thickness, resulting in charge appearing only on parallel faces.The net flux through the gaussian surface will be zero because the field lines are parallel, and surfaces (1) and (2) will be inside the conductor’s substance.

As a result, the net charge enclosed will be zero, implying that the charges on the confronting surfaces are equal and opposing each other.

At any point ‘P’ or ‘R,’ the net electric field must be zero.

(Enet )P=0

There are four distributions, each with a net field of zero at P.

-E.Q.

Note:

When charged conducting plates are arranged parallel to each other, the two outermost surfaces are charged equally, and the surfaces that confront each other are charged equally and oppositely.

Force on a Charged conductor

Imagine a small segment X.Y. being cut and removed from the remainder of the conductor M.L.N. to find the force on a charged conductor (due to repulsion of like charges). The cavity field owing to the rest of the conductor is E2, whereas the cavity field due to the little component is E. Then, Inside the conductor

.-E.Q.

Outside the conductor -EQ

Imagine a charged part X.Y. (with charge dA) inserted in a cavity M.N. with field E2 to find force. As a result, force is used. -E.Q.

(Electrostatic pressure is a term that refers to the pressure between two points. Because (±σ)2 is positive, the force is always outwards, attempting to expand the positively or negatively charged body.

When a soap bubble or rubber balloon is given a charge (of any kind + or -), it expands.

capacitors capacitors

Capacitance

Definition

We know that applying a charge to a conductor raises its potential, i.e., Q∝V⇒Q=CV Where C is a proportionality constant, also known as conductor capacity or capacitance. As a result, capacitance refers to a conductor’s ability to hold a charge (and associated electrical energy).

Unit and Dimensional Formula

-E.Q.

mF, F, nF, and pF are smaller S.I. units.

-E.Q.

Stat Farad is a C.G.S. unit. Stat Farad F=9×1011

Capacitor

Definition

A capacitor is an electric energy storage device. The condenser is another name for it, or a capacitor is made up of two conductors of any kind that are near together and have the same and opposing charge.

Symbol

The symbol of the capacitor is shown below:

Capacitance

A capacitor’s capacitance is equal to the magnitude of the charge Q on the positive plate divided by the magnitude of the potential difference V between the plates, or C=Q/V.

Note:

For the specified size and medium, a capacitor’s capacitance is constant.

2.4 Charge on Capacitor

A capacitor’s net charge is always zero, but when we talk about the charge Q, we’re talking about the size of the charge on each plate.

2.5 Energy Stored

A capacitor retains electric energy when a voltage source (such as a battery) is charged.

The density of energy:  U/vol 

Density energy = 12𝛆o E2

If C is the capacitor’s capacitance, Q is the charge on the capacitor, and V is the potential difference across the capacitor. The energy stored in the capacitor is U.

U = 12C V2

Note:

Half of the energy supplied is stored in the capacitor when a battery charges it, and the other half (1/2QV) is lost as heat.

2.7 Capacity of an Isolated Spherical Conductor

When a spherical conductor of radius R is charged with Q, the potential at the surface of the sphere is V = 14OQR

3. Properties of an Ideal Battery

(a) There are two terminals on a battery.

(b) The potential difference V between the terminals is constant for a given battery. The positive terminal has a higher potential than the negative terminal, whereas the negative terminal has a lower potential.

(c) The battery’s electromotive force, or emf, is equal to the value of this fixed potential difference. When a conductor is connected to a battery terminal, the conductor’s potential is equal to the terminal’s potential. When the two plates of a capacitor are connected to the terminals of a battery, the potential difference between the plates is equal to the battery’s emf.

(d) A battery’s overall charge always remains zero. If the positive terminal of the device generates a charge Q, the negative terminal generates a negative charge Q.

(e) When a charge Q flows from the negative terminal to the positive terminal of an emf E battery, the battery performs an amount Q.E. of work. The symbol depicted in the figure represents an ideal battery. The emf of the battery is equal to the potential difference between the two parallel lines. The larger the potential, the longer the line.

6. Dielectric

Dielectrics are insulating (non-conducting) materials that convey electric signals without electricity. As we all know, every atom has a positively charged nucleus and a negatively charged electron cloud. Each of the two oppositely charged zones has its own charge centre. The nucleus positive charge centre is the positively charged protons’ mass centre. The centre of mass of negatively charged electrons in atoms/molecules is known as the negative charge centre.

6.2 Dielectric Constant

After a dielectric slab has been placed in an electric field, the net field in that area is reduced.

If E is the original electric field and Enet equals the net electric field,

Then, EEnet = K

K stands for the dielectric constant. K is also known as the material’s relative permittivity (r).

6.3 Dielectric Breakdown and Dielectric Strength

When a dielectric is subjected to a strong electric field, the outer electrons may separate from their parent atoms. The dielectric then takes on the properties of a conductor. Dielectric breakdown is the term for this event.

The dielectric strength of a dielectric material refers to the greatest value of the electric field (or potential gradient) that it can endure before breaking down.

The SI measure for dielectric strength is V/m, whereas the practical value is kV/mm.

6.4 Variation of Different Variables (Q, C, V, E and U) of Parallel Plate Capacitor

Assume we have an air-filled, charged parallel plate capacitor with the following variables:

Q’s charge

Surface charge density: – 𝛔 = QA

Capacitance: – C = oAd

The potential difference across the plates: – V = E.d

The electric field between the plates: – E = o = QAo

Energy stored: – U = 12CV2

Note:

If nothing is said, the battery is considered disconnected.

7. Van De Graff Electrostatic Generator

A Van de Graff generator is a device that generates huge potential differences in the millions of volt range. High potential differences are used to accelerate charged particles such as electrons, protons, and ions, which are required for many nuclear physics studies. In the year 1931, Van de Graff designed it.

This generator is based on the following principle.

The phenomenon of corona discharge is caused by sharp points.

(ii) the property of a hollow conductor charge being transferred to its outer surface and dispersed uniformly throughout it.

The key components of the Vat de Graaff generator are a big spherical conducting shell with a few metres in radius. A conductive shell with a radius of a few metres supports this. This is supported over the insulating pillars P1 and P2 at a sufficient height (several metres above the ground). Two pulleys are wrapped in a long, thin belt of insulating material such as silk, rubber, or rayon. P1 and P2 are at ground level, while P2 is in the centre of S. With the help of a motor, the belt is kept moving continually over the pulleys (not shown). Two finely pointed metal combs, B1 and B2, are fixed as indicated. B1 is known as the spray comb, whereas B3 is known as the collecting comb.

In a discharge tube D, the positive ions to be accelerated are created. Inside the spherical shell, the ion source is located at the tube’s head. The target nucleus is carried in a tube with one end earthed.

To prevent leakage in a steel spherical conductor, the generator is encased in a steel chamber C filled with nitrogen or methane under high pressure. Working: High tension source H.T. provides a positive potential (104 volts) to the spray comb about the earth. A positively charged electric wind is created from the sharp needles discharging, spraying a positive charge on the belt (corona discharge). A negative charge is induced on the sharp ends of collecting comb B2, and an equivalent positive charge is produced on the farther end of B2 as the belt travels and reaches the comb. This positive charge is promptly transferred to S’s outer surface. A negatively charged electric wind is created because of the sharp tips of B2 discharging. This cancels out the belt’s positive charge. The uncharged belt descends, collecting the positive charge from B1 and passing it on to B2. This happens again and again. As a result, the positive charge on S continues to accumulate.

Now, c=40R, where R is the shell’s radius and the spherical shell capacity.

As,  V = QC 

V = Q4oR

Air has a breakdown field of roughly 3106V/m. When the potential of the spherical shell surpasses this amount, the air around S becomes ionised, and charge leaking begins. The generator assembly is housed inside a steel container filled with nitrogen or methane at high pressures to reduce leaking.

If q is the charge on the accelerated ion and V is the potential difference formed across the discharge tube’s ends, then the ions’ energy is equal to qV. With this energy, the ions strike the target and perform artificial transmutation, for example.

8. Combination of Drops

Assume we have n identical drops, each with the following characteristics: radius r, capacitance c, charge q, potential v, and energy u.

When these drops are merged to make a large drop of Radius R, Capacitance C, Charge Q, Potential V, and Energy U, the result is –

I Charge on a significant drop:

Q=nq

(ii) Big Drop Radius:

The volume of a large drop equals the volume of a single drop, i.e.

43R3 = n x 43r3 ,

Where R = n1/3r

(iii) Capacitance of big drop:

C = n1/3c

(iv) Potential of big drop:

V = QC = nqn1/3c

V = n2/3v

(v) Energy of big drop:

U = 12CV2 

U = n5/3u

Note:

A common misunderstanding is that a capacitor stores charge, whereas it actually stores electric energy in the electrostatic field between the plates.

Because the effective overlapping area is taken into account, two uneven area plates can also form a capacitor.

The effective overlapping area of plates (C.A.), the gap between the plates (C1/d), and the dielectric medium filled between the plates determine the capacitance of a parallel plate capacitor. It is unaffected by the charge applied, the potential raised, the composition of the metal, oror the plates’ thickness.

To avoid fringing or edge effects (non-uniformity of the field) at the plate boundaries, the distance between the plates is kept modest.

A spherical conductor is the same as a spherical capacitor with an unlimited outer sphere.

If the spherical surfaces of a spherical capacitor have high radii and are close to one another, it functions like a parallel plate capacitor.

The distance between the plates of a parallel plate capacitor (E=/0) does not affect the intensity of the electric field between them.

Between the spherical surfaces of a spherical capacitor, there is a radial and non-uniform electric field.

(Method of CircuitSolving)

Finding the equivalent capacitance of a combination using the equations for series-parallel combinations might take time and effort. Then we can use the following generic method:

1st Step:

Determine the two sites where the equivalent capacitance must be determined. Anyone can be referred to as A, while the other is referred to as B.

Step two:

Connect a battery to A and B (mentally), with the positive terminal to A, and the negative terminal to B. Charge the battery by sending a charge +Q from the positive terminal and a charge Q from the negative terminal.

3rd Step:

Make a list of the charges that appear on each of the capacitor plates. It’s possible to employ the charge conservation concept. A capacitor’s facing surfaces will always have equal and opposite charges. Assume variables Q1, Q2, and so on for charges wherever needed. Mark the polarity of each circuit element for the higher (+) and lower (-) potential ends, respectively.

4th Step:

The algebraic total of all potential differences in a circuit’s closed loop is zero.

When applying this rule, one begins at a location on the loop and works their way clockwise or anticlockwise around the loop until they reach the same position. Any possible difference (from -ve to +ve) is considered good, whereas any potential decrease (from +ve to -ve) is considered negative. All of these potential disparities should add up to zero.

The loop law is based on the idea that electrostatic force is a conservative force that does no work in any closed path.

5th Step:

The number of variables (Q1, Q2, and so on) mustequal the number of equations found (loop equation). Again, the equivalent capacitance. Ceq = Q/V, where V denotes the assumed potential difference between the battery terminals.

 

10. Wheatstone Bridge-Based Circuit

Wheatstone bridge-type circuits are created when four capacitors are arranged in a network, as shown in the following diagram. If it’s balanced, that’s great.

C1C2 =C3C4

By balancing two legs of the bridge circuit, the Wheatstone bridge, also known as the resistance bridge, determines the unknown resistance. One of the legs has an unknown resistance component. In 1833, Samuel Hunter Christie designed the Wheatstone bridge, popularised by Sir Charles Wheatstone in 1843.

The Wheatstone Bridge Circuit consists of a bridge formed by two known resistors, one unknown resistor, and one variable resistor. This bridge is extremely dependable since it provides precise measurements.

11. Extended Wheatstone Bridge

In the illustration, two wheatstone bridges are connected.One bridge connects the points AEGHFA and EGBHFE, while the other connects the points AEGHFA and EGBHFE. This problem is known as the extended Wheatstone bridge problem because it has two branches, E.F. and G.H., to the left and right, of which there is symmetry in the capacity ratio.

The ratio of capacitances in branches A.E. and E.G. is the same as the ratio of capacitances in branches A.F. and F.H. As a result, branch E.F. can be removed from the AEGHFA bridge. G.H. can also be removed from the EGBHFE branch of the bridge.

CAB = 2C3

12. Infinite Network of Capacitors

I Assume the effective capacitance between A and B is CP: Because the network is infinite, even if one pair of capacitors is removed from the chain, the remaining network has an infinite number of capacitors. Hence the effective capacitance between X and I is also C.R.

As a result, A and B have comparable capacitance.

CAB = C1 (C2 + CR)C1 +C2 + CR = CR

CAB = C22[(1 + 4C1C2) -1 ] 

(ii) In the circuit shown above, for what value of C0 would the net effective capacitance between A and B be independent of the number of sections in the chain? Assume that C0 terminates the network with equivalent capacitance C.R. ′ and that there are n sections connecting A and B.Now, if we add one more section to the network between D and C (as indicated in the diagram), the equivalent capacitance of the network C.R. will be independent of the number of sections as long as the capacitance between D and C stays C0, i.e.,

C0 = C22[(1 + 4C1C2) -1 ]

13. Circuits With Extra Wire (plate numbering method)

If no capacitor is present in any branch of a network, every point on that branch will have the same potential. Consider the following scenarios for determining comparable capacitance.

14. Using Symmetry Between Two Points

1. Symmetry is always described as a relationship between two points.

2 Equivalent (symmetric) pathways include the same number, value, and order of circuit elements.

3. Charges flowing over two or more paths in a network will be the same if they are equal. This method makes the circuit simple to understand.

15. Battery Superposition Method15. Battery Superposition Method

The charge flowing in a circuit with many batteries is due to the superposition effect of each battery.

The impact of a 10V battery

The impact of a 5-volt battery

Effects when used together

Note:

Take the individual effect of each battery when more than two are present, assuming the other batteries are not there. Then, to obtain the overall effect, superimpose.

16. Dielectric

16.1 Series and Parallel (With Dielectrics)

H4 -16.2 When Separation Between the Plates Is Changing

According to C1d, if the gap between the plates changes, the capacitance also changes. The impact on other variables is determined by whether the charged capacitor is detached from the battery or is still attached to the battery.

16.3 Force on Dielectric

Due to the fringing field just outside the plates, when the dielectric is placed near the charged capacitor (rectangular plates), it experiences force toward the capacitor.

(a) Battery is plugged in (V remains same)

F = 12 o b V2(K-1)d (towards capacitor)

Note:

The amount of dielectric between the plates has no bearing on the force-Additivity of Charges

When the dielectric is in the middle of the plates, the force is zero.

(b) Disconnecting the battery (Q remains the same)

F = 12 Q2d (K-1)2o b ( l + x(K-1))2

Note:

Force is determined by  x (the amount dielectric inside the capacitor plates).

17. Redistribution of Charge Between Two Capacitors

When a charged capacitor is linked across an uncharged capacitor, the charge is redistributed to balance the potential difference between the two capacitors. Heat is another way that energy is wasted.

After detaching C1 and C2 from their respective batteries, we have two charged capacitors, C1 and C2. The connections between these two capacitors are given below (the positive plate of one capacitor is connected to the positive plate of the other, while the negative plate of one is connected to the negative plate of the other).

The charge on the capacitors will be redistributed, and a new charge will be placed on them.

Q1l =Q (C1C1 + C2) 

Q2l =Q (C2C1 + C2)

Note:

Two capacitors with C1 and C2 are charged to V.L. and V2 potentials, respectively. They are reconnected to each other with reverse polarity after being disconnected from the batteries, with the positive plate of one capacitor linked to the negative plate of the other. As a result, the most common potential w charge on them will be 

V = Q1 +Q2C1 + C2 = C1V1 + C2V2C1 + C2

Quantisation of Charge

Electric charge quantisation is an attribute in which all free charges are an integral multiple of e, the basic charge unit. The charge (q) of a body is calculated as follows:

 q =± ne    

The letters + e and – e stand for proton and electron, respectively.

Additivity of Charges

The algebraic sum of all the individual charges in the system equals the overall charge. Consider a charging system with three-point charges of magnitude q1, q2, and q3. The overall charge of the system can be calculated by summing the three charges algebraically.

-E.Q.

These charges have magnitude but no direction, are scalar quantities and should be considered real numbers when performing any operation. The total charge of a system containing n particles can be written as follows:

-E.Q.

We should notice that the charge might be positive or negative, and the operation considers the charge’s sign.

Conservation of Charge

In an isolated system, the full charge is conserved.

When you brush the rod with silk, the silk gains the charge while the rod loses it.

Coulomb’s Law

Coulomb’s Law describes the attraction or repulsion force between two-point charges. This force is proportional to the product of their products and inversely proportional to the square of their distance apart.

This force acts along the line that connects the two charges’ centres. It is provided by:

-E.Q.

k is the electrostatic force constant and equals

-E.Q.

0 is the free space permittivity, which has a value of 8.85 x 10-12C2N-1 m-2 and a dimension of [M-1L-3T4A2].

Properties of Electric Field Lines

(a)Electric Field lines can’t form closed loops because they’re unending curves.

(b)They are inextricably intertwined.

(c)Positive charges initiate electric field lines, which end at negative charges.

Electric Field Due to Dipole

The electric field strength due to a dipole far away is always proportional to the dipole moment and inversely proportional to the cube of the distance. The dipole moment is the product of the charge and the distance between the two charges.

-E.Q.

Gauss Law

The total electric flux out of a Gaussian surface equals the integration of the net charge enclosed in this surface divided by the permittivity of free space, according to Gauss’ Law. Its formula is as follows:

E . dA = Qeno

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