A solid sphere of radius R has a charge `+2Q`. A hollow spherical concentric with the first sphere that has net charge -Q.

(a) Find the electric field between the spheres at a distance r from the centre of the inner sphere. `[R ltr lt3R]`
(b) Calculate the potential difference between the spheres.
(c) What would be the final distribution of charges, if a conducting wire joins the spheres?
(d) Instead of (c), if the inner sphere is earthed, what is the charge on it?

Answer

C, D

Explanation

a. From Gauss's theorem
`E=(1/(4piepsilon_0))(q_("in")/r^2)=(1/(4piepsilon_0))((2Q)/r^2)`
`=Q/2piepsilon_0r^2)`
b. According to principle of generator, potential difference depends only on `q_("in")`
`:. PD=(2theta)/(4piepsilon_0)(1/R-1/(3R))=Q/(3piepsilon_0R)`
c. According to priniple of generator, whole inner charge transfers to outer sphere.
d. `V_("in")=0`
`:. (kq_("in"))/R-(kQ)/(3R)=0implies q_("in")=Q/3`