Current Density Formula

Current Density Formula

Current density is defined as the amount of current flowing per unit area of the wire. It is measured in amperes per square metre. Before knowing more about current density, we must first understand current.

Current is defined as the passage of electrons over a wire under a voltage differential. Current is the most frequent sort of energy utilised in our everyday lives; it produces electrical energy that powers all of the electrical equipment we use every day.

In this post, we will learn about current density, its formula, derivation, and a quick overview of electric current.

Formula of Current Density

Electromagnetism is closely connected to current density or electric current density. It is defined as the amount of electric current flowing through a unit value of a cross-sectional area. When a constant current runs through a conductor, the same current flows through all of the conductor’s cross-sections. Even though the cross-sections change in size, the flow is the same. A macroscopic entity is an electric current. One makes assumptions about electric current flowing via a conductor rather than the electric current flowing through a point. The Current Density Formula is a comparable microscopic in the electrical field.

The formula for calculating the current is,

i = q/t

where,
i is the current,
q is charge following in the conductor,
t is the time taken

The current density formula is as follows:

J = I/A

where,

• J is the Current Density (A/m²)
• I is the flow of current through the conductor (A)

• A is the Cross sectional area (m²)

What is the current density?

In a conductor, current strength is defined as the rate of charge flow through any cross-section of the conductor. An electric current is commonly thought of as a flow of electrons. Electrons flow out of one end of a battery, via the wire, and into the other end of the battery when two ends of a battery are connected by metal wire. Current is considered steady if its magnitude remains constant and its direction remains constant.

The density of current flow in a conductor is referred to as its current density. It is represented by the letter J. Current Density and its measurement are critical in the science of Electromagnetism. It is the flow of electric charge measured in amperes per unit area of cross-section, i.e. m2. This is a vector quantity since the magnitude is accompanied by the direction of flow. A flowing electrical current with units of charge per unit time per unit area. It is also measured in the perpendicular direction to the flow of direction.

Ampere per square metre is the unit of electric current density. The Current Density Formula is the measurement of electric current in the study of electromagnetism. It refers to the quantity of current moving through a certain region.

Derivation of Current Density Formula

The current density formula is based on the definition of current density. We know that the current density is defined as the current flowing through the per unit area of the conductor, hence,

J = dI/dA

where,
dI/dA is the Current change with the unit area.

which implies,

dI = J × dA

dI = J × dAcosθ

when
dA is perpendicular to J,   (if θ = 90^o so, cos θ = 1).

Therefore,

dI = J × dA

integrating both sides

∫₀ ^J dI = J × ∫₀ ^A dA

I = J×A

J = I/A

Solved Examples

Example 1: A copper wire with a diameter of 6 mm² has a current of 12 mA flowing through it. Calculate the current density of the conductor.

Solution:

Given,

A = 6 mm² = 0.000006 m²,

I = 12 mA = 0.012 A

Since,

J = I/A

J = 0.012 / 0.000006

J = 200 A/m²

Example 2: If the current density is 8 A/m² and the current through the conductor is 32 A. Calculate the cross-sectional area.

Solution:

Given,

J = 8 A/m²

I = 32 A

Since,

J = I/A

A = I/J

   = 32/8

  = 4 m²