Two concentric hollow spherical shells have radii r and R(R >> r). A charge Q is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

Options

A. `Q(R + r)/4pi epsilon_(0)(R^(2) + r^(2))`
B. `Q(R_(2)+ r_(2))/4pi epsilon_(0)(R + r)`
C. `Q/(R +r)`
D. Zero

Answer

(a)

Explanation

The surface charge densities is `sigma` = `Q/ 4pi (r^(2) + R^(2))`
Electric potential at the center is ,
`V = 1/4pi epsilon_(0) [sigma xx 4 pi r^(2)/r + sigma xx 4 pi R^(2)/R]`
` V = !/ 4 pi epsilon_(0)(r^(2) + R^(2)) (r +R) = Q(r + R )/4 pi epsilon_(0)(r^(2) + R^(2))`