Current Density | Definition | Formula

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Electric Current-

 

Before you go through this article, make sure that you have gone through the previous article on Electric Current.

 

We have learnt-

  • Electric current is the flow of electric charges through a conductor in a preferred direction.
  • Quantitatively, it is the amount of charge flowing through the cross-sectional area of conductor per unit time.

 

In this article, we will learn about current density.

 

Current Density-

 

Electric current may be distributed non-uniformly over the surface through which it passes.

Hence to characterize current in greater detail, the concept of current density is introduced.

 

The current density at any point inside a conductor across an area held perpendicular to the direction of flow of charges is defined as the amount of charge flowing per unit area.

 

It is a vector quantity having the same direction as that of electric current.

 

Case-01:

 

Consider current I is flowing uniformly and normally through an area of cross-section A as shown-

 

 

In this case, the magnitude of current density at any point of this cross-section is given by-

 

 

Case-02:

 

Consider the area A is not perpendicular to the direction of electric current and its area vector makes an angle θ with the direction of current as shown-

 

 

Here, the effective area which is perpendicular to the direction of flow of charges is the component of area having area vector = Acosθ.

 

In this case, the magnitude of current density at any point of this cross-section is given by-

 

 

This formula can also be written as-

 

 

This is a general relation between electric current and current density.

 

Characteristics of Current Density-

 

  • It is a characteristic of any point inside the conductor.
  • It is more fundamental than electric current as it is area independent.
  • Its SI unit is ampere per square meter (Am-2).
  • Its dimensional formula is [M0L-2T0A1].
  • It is a vector quantity having its direction same as direction of electric current.

 

Electric Current Vs Current Density-

 

Electric Current

Current Density

It is always defined for an area and not a point. It is always defined for a point and not an area.
It is a scalar quantity. It is a vector quantity.
It is denoted by the symbol I. It is denoted by the symbol j.
Its SI unit is ampere (A). Its SI unit is ampere per square meter (Am-2).

 

Important Note-

 

In steady state, the electric current flowing through each cross-section of the conductor is same i.e.

I = constant

In other words,

jA = constant
Or
j1A1 = j2A2

 

This relation helps to compare the current densities through cross-sections of different areas.

 

Read the next article on-

Drift Velocity & Relaxation Time

 

Get more notes & other study material of the Chapter Current Electricity.


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