## Current And Current Density

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# Current and Current Density

**Electric Current.**In an isolated metallic conductor, the free electrons present in it are in random motion like the molecules of a gas. So the net rate at which electrons passes through any hypothetical plane in zero. It the through any hypothetical plane is zero. If the ends of the conductor are connected to a battery, an electric field E will be set up at every point within the conductor. This field acts on the electrons and gives them a resultant motion in the direction – E. If a charge q passes through any cross-section of the conductor in time t, then the current i is defined by

I = q/t

When q is in coulomb and t in second, then i is in amprere. If the rate of flow of charge with time is not constant the current varies with time. Then at any instant t current is defined as the net charge flowing across the area per unit time. Current is a scalar quantity. Conventionally, the direction of electric current is taken along the direction of motion of positive charges. When the current is opposite to the direction of electron flow.

**Current density.**Current is a macroscopic quantity. The related microscopic quantity is the current density J.

The current density at any point is defined as the quantity of charge passing per second through a unit area taken perpendicular to the direction of the flow of charge at that points on that cross section is given by

J =

__q/t__=

__i__

A A

The unit of current density is A/m

^{2}.

Current i is related to the current density

**J**by

i = ∫

**J**. d

**S**

Where dS is an element of area and the integral is taken over any surface cutting across the conductor.

From this equation we may define the current i as the flux of the current density vector

**J**through a given area.

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