Question

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 electric field `vec(E)` in the overlapped region is
A. nonuniform
B. zero
C. `(rho)/( 3 epsilon_(0)) vec(d)`
D. `(-rho)/( 3 epsilon_(0)) vec(d)`

Answer 1

Correct Answer - C
Take a point `P` in overlap region , then
`vec(E )_(p) = ( rho vec (r_(1)))/( 3 epsilon_(0)) - ( rho vec (r_(2)))/( 3 epsilon_(0))`
` = (rho)/( 3 epsilon_(0)) ( vec(r_(1)) - vec (r_(2))) = ( rho vec (d))/( 3 epsilon_(0))`
This is the uniform field in overlap region.