There are two nonconducting spheres having uniform volume charge densities `rho` and `- rho` . Both spheres have equal radius `R`. The spheres are now laid down such that they overlap as shown in Fig.2.125. Take `vec(d) = O_(1) vec(O_(2))`.

The potential difference `Delta V` between the centres of the two spheres for `d = R` is

Options

A. `(rho)/(3in_(0))d^(2)`
B. `(rho)/(in_(0))d^(2)`
C. zero
D. `(2ho)/(in_(0))d^(2)`

Explanation

`int_(v_(1))^(v_(2))V=-int_(0)^(d)(rhod)/(3epsilon_(0))dx,V_(2)-V_(1)=-(rhod^(2))/(3epsilon_(0)),|triangleV|=(rhod^(2))/(3epsilon_(0))`