Current Density Formula

Current density or electric current density is very much related to electromagnetism. It is defined as the amount of electric current flowing through a unit value of the cross-sectional area. In case of a steady current that is flowing through a conductor, the same current flows through all the cross-sections of the conductor. This flow is the same even though the cross-sections may differ in area. Electric current is a macroscopic entity. We assume about the electric current through a conductor and not about electric current at a point. A corresponding microscopic, in the electricity field, is current density. In this article, we will discuss the current density formula with examples. Let us begin learning!

Current Density Formula

What is the current density?

Current strength, in a conductor, can be defined as the rate of flow of charge across any cross-section of the conductor. An electric current is usually considered as a flow of electrons. When two ends of a battery are connected to each other by using metal wire, electrons flow out of one end of the battery, through the wire, and into the other end of the battery. Current is usually steady if its magnitude is constant and its direction will always be the same.

Current density refers to the density of current flow in some conductor. It is denoted by the symbol J. In the field of electromagnetism, Current Density and its measurement is very important. It is the measure of the flow of electric charge in amperes per unit area of cross-section i.e. m². This is a vector quantity because with the magnitude it is having the direction of flow. An electrical current that flows through and has units of charge per unit time per unit area. It is also measured in the direction which is perpendicular to the flow of direction.

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The unit of electric current density is denoted as ampere per square meter. In the study of electromagnetism, Current Density is the measurement of electric current. It concerns the amount of current flowing across the given area.

Suppose a medium (conducting material) has an electric conductivity given by $$\sigma$$. Then the electric current density can be related with the Electric Field by the equation:

J = Σ × E

Where,

J	Current density
\sigma	Conductivity
E	Electric field

In another way,

Current Density Formula can be expressed as,

J =\( \frac{I}{A} \)

Where,

J	Current density in A/m^2
A	The cross-section area in m^2
I	Current flowing through the conductor in Amperes

Solved examples:

Q.1: A 15 mm² copper wire has a current of 5 mA of current, which is flowing through it. Find out the current density.

Solution:

The Given parameters are:

Total Current,

I = 5 mA

Total Area,  A =  15 mm²

The Current density  formula as,

J = \( \frac{I}{A} \)

J =  \( \frac{5× 10^{-3}}{15 ×10^{-3}}\)

J=0.33 A/m²

Thus current density is 0.33 A/m²

Q.2: Determine the current density of 100 Amperes of current is flows through the battery in an area of 10 m² ?

Solution

Given parameters

Current I = 100 A,

Area, A = 10 m²

Now, applying the formula,

J = \( \frac{I}{A} \)

J = \( \frac{100}{10}\)

= 10 A/m²

 Thus current density is 10 A/m².