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

Options

A. non uniform
B. zero
C. `(rho)/(3in_(0))d`
D. `(rho)/(3in_(0))R`

Explanation

`vecE=(kQ)/(x^(2))`
`vecE_(1)=(1)/(4piepsilon_(0))((4)/(3)pix^(3))/(x^(2))=(rhod)/(3epsilon_(0))(d-x)`
`E_("net")=E_(1)+E_(2)=(rho(d-x))/(3epsilon_(0))+(rhox)/(3epsilon_(0))` ltrgt `E=(rhod)/(3epsilon_(0))`