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)/( 3 epsilon _(0)) d^(2)`
B. `(rho)/( epsilon_(0)) vec(d^(2))`
C. zero
D. `( 2rho)/( epsilon_(0)) d^(2)`

Answer

A

Explanation

`d = R`
Electric field from `O_(1)` through `O_(2)` is uniform and is `E = rho R//3 epsilon_(0)`.
So potential difference is
`Delta V = ER = ( rho R^(2))/( 3 epsilon_(0)) = ( rho d^(2))/( 3 epsilon_(0))`