Two connectric spheres of radii `R` and `r` have similar charges with equal surface charge densities `(sigam)`. The electric potential at their common centre is

Options

A. `sigma//epsilon_(0)`
B. `(sigma)/(epsilon_(0))(R-r)`
C. `(sigma)/(epsilon_(0))(R+r)`
D. None of these

Answer

C

Explanation

Charge on the outer spehre `q_(1)=4piR^(2) sigma`
Charge on the oute `=q_(2)=4pir^(2)sigma`
`v=1/(4 pi epsilon_(0))(q_(1))/R+1/(4pi epsilon_(0))(q_(2))/r`
`=1/(4piepsilon_(0))[(4piR^(2)sigma)/R+(4pir^(2)sigma)/R+(4piR^(2)sigma)/r]=(4pisigma)/(4piepsilon_(0))(R+r)=(sigma)/(epsilon_(0))(R+r)`