The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume charge density `p =(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 :

Answer

A, B, C

Explanation

Net charge between r=a to r=r would be `Q=int_a^r rho(4pir^2)dr=int_a^4C/r(4pier^2)dr`.
`Q=2piC(r^2-a^2)`
`E_r=(k(Q+q))/r^2=(k[2piC(r^2-a^2)+q)]/r^2`
From this expression we can see that it we put
`C=q/(2pia^2)`
`E_r=(kq)/a^2=0`constant