A uniform electric field in positive `x`-direction on exists in space. An uncharged solid conducting sphere is now placed in region of this uniform electric field. The centre of this sphere of radius `R` lies at origin. Then electric potential at any point on `y-z` plane (i.e. `x=0` plane) due to only induced charged on surface of sphere.

Options

A. will be positive
B. will be negative
C. will be zero
D. may be positive, zero or negative

Answer

C

Explanation

The induced charge on conducting sphere are symmetrical with respect to yz plane as shown. The induced charge is equivalent to a dipole along x-axis and y-z plane is the equatorial plane of dipole. Therefore potential at each point on y-z plane due to induced charges is zero.