A charge Q is distributed over two concentric hollow spheres of radii r and `R (gt r)` such that the surface charge densities are equal. Find the potential at the common centre.

Options

A. `1/(4piepsilon_(0)) ((2R +r))/((R^(2)+r^(2))) Q`
B. `1/(4piepsilon_(0)) ((R+r))/((R^(2)+r^(2)) )Q`
C. ` 1/(4piepsilon_(0)) ((R+r))/(2(R^(2)+r^(2)))Q`
D. `1/(4piepsilon_(0)) ((R+2r)Q)/(2(R^(2)+r^(2)))`

Answer

B

Explanation

`Q_(1) = sigma .4 pir^(2)`
` Q_(2) = sigma .4piR^(2) `
`Q = 4pisigma (R^(2) +r^(2))`
` rArr sigma = Q/(4pi(R^(2)+r^(2))`
` v_(e) = (KQ)/r + (KQ_(2))/R`
` == (Ksigma 4pir^(2))/r = (Ksigma 4piR^(2))/R = K sigma 4pi (r+R)`
` 4 piK Q/(4pi(R^(2)+r^(2))) (r+Q) = (KQ (r+Q))/((R^(2)+r^(2))`