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 Id is the displacement current,ϕE is the varying electric flux


through the area and ϵ0 is the electric permittivity of free


space(vacuum) and is equal to 8.85 × 10-12 C2 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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