The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), have volume charge density `rho=A/r`, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

Options

A. `(2Q)/(pia^(2))`
B. `Q/(2pia^(2))`
C. `Q/(2pi(b^(2)-a^(2)))`
D. `(2Q)/(pi(a^(2)-b^(2)))`

Answer

B

Explanation

Gaussian surface at distance r from center
`(Q+underset(a)overset(r)(int)A/r 4pir^(2)dr)/in_(0)=E4pi r^(2)`
`E=(Q+2pi Ar^(2)-2piAa^(2))/(4pir^(2) in_(0))`
make E independent of r then
`Q-2pia^(2)A=0 rArr A=Q/(2pia^(2))`