Q. 25.0( 1 Vote )

# A point charge is

Answer :

Given: Velocity of charge = v

Area of patch = A

Distance of charge from the patch=x

We have to find the displacement current through the area when it is at a distance x from the charge.

The displacement current arises due to changing electric field which in turn produces a varying electric flux through an area. The displacement current depends on the electric flux as

where I_{d} is the displacement current,*ϕ*_{E} is the varying electric flux

through the area and *ϵ*_{0} is the electric permittivity of free

space(vacuum) and is equal to 8.85 × 10^{-12} C^{2} N^{-1} m^{-2}.

The electric field produced by the charge when it is at a distance x

from the surface is given by Coulumb’s law and is equal to

This electric field produces an electric flux through the area whose

magnitude is given by Gauss’s law

. This is because the electric field lines are directed along the normal to the area vector of the surface.

The angle θ between them is 0^{°} so cos 0^{°} =1.

The displacement current will be

As x is the distance of the charge from the area at different intervals of time so the rate at which the particle is changing its position is its velocity v

Thus the displacement current through the area is

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