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Home / Physics / Current Density

Current Density: Definition, Formula, Current Density-Electric Field Relation & Solved Examples

Last Updated on Feb 19, 2025
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An electric current is the flow of charge carriers in a conducting material usually due to the presence of electrons in it, which are negatively charged particles of an atom, or due to electron-deficient atoms present in it, which are responsible for making an atom positively charged. Current density is the measure of the amount of current flowing through the given area.

In this article, we will be learning about current density, current density formula, units of current density, dimensional formula of current density, the relation between current density and electric field, and some of the solved examples of current density along with some FAQs.

Current Density

Current Density is the amount of electric current which can travel per unit of a cross-section area. The more the current is present in a conductor, the higher the current density will be. Regardless, the current density always changes in different parts of an electrical conductor and the effect of it takes place with higher frequencies in alternating current.

Electric current always creates a magnetic field. The stronger the current, the more intense the magnetic field will be. Varying alternating current or direct current creates an electromagnetic field and this is the principle on which signal propagation taking place is based through the magnetic effect of electric current.

The symbol by which the current density is denoted is J. It is a vector quantity having both a magnitude as well as a direction.

The direction of a current density is the same as the direct motion of a positive charge or a positively charged atom. In general, we can say that the current density is all about the amount of electric current flowing across the given area.

Current Density Formula

The formula of the current density is represented by the equation given below:

  • Where I is the current flowing through the conducting material.
  • A is the area of the cross-section of the conducting material.

The unit or SI unit of the current density is Amperes per square meter, which can be written as

Therefore, the dimensional formula of the current density will be represented

Which can be simplified as .

Relation between Current Density and Electric Field

The relation between Current Density and Electric Field can be described as follows,

Since we know that current density is a vector quantity which is defined as the electric current flowing per unit area of a material which is measured in a direction normal to the direction of flow of the electric charge. It is represented as,

Since we know that

And

We also know that

Now substituting the value of R in the equation of finding I.

We get,

Now put the new value of I in the equation of finding J, which is the current density, we get,

Therefore, we get now,

 

Which is equal to,

  • Where σ is the conductivity of the conducting material.
  • E is the produced Electric Field.

Therefore, the above end equation signifies that J which is current density is directly proportional to E which is the electric field.

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Solved Examples of Current Density

Example 1.What is the density when 137 Ampere of current flows through a conductor of cross-section, measuring ?

Solution. Given,

Since we know that,

So,

Therefore,

 

.

Example 2. Determine the current density if 50 Amperes of current flows through the battery in an area of ?

Solution. Given,

Since we know that,

Therefore,

.

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Current Density FAQs

The unit of the current density is Amperes per square meter, which can be written as,.

The current density of copper will be calculated by putting the value of its area of cross-section and the value of its electric current in the below formula..

Yes, the current density is a vector quantity as it has both magnitudes as well as directions.

No, the current density is not the same as voltage but we can say that both are analogous to each other as current density is directly proportional to the voltage.

The current density can be defined as the amount of electric current which can travel per unit of a cross-section area.
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