A solid sphere of radius `r_1` =1 cm carries charge distributed uniformly over it with density `rho_1 = -3 C//cm^3` . It is surrounded by a concentric spherical shell of radius `r_2 = 2cm` carrying uniform charge density `rho_2 = 1/2 C//cm^2` . If `E_d` denotes the magnitude of the electric field at distance d from the common centre of the spheres, then

Options

A. `E_d = (1)/(3epsi_0 d^2) d lt= 1cm `
B. `(1)/(epsi_0 d^2) d lt= 1cm`
C. `E_d = (d)/(3 epsi_0) d lt= 1 cm`
D. `E_d = (d)/(epsi_0) , d lt= 1cm `

Answer

D

Explanation

Electric field at a point inside inner sphere is only due to charge enclosed. We use Gauss. law to get,
` E = ( (q)/(4pi epsi_0 R^3) ) r = (rho_R)/(3 epsi_0 )`
Here , ` rho = - ( (C)/(cm^3) )`
so , ` E = (-d)/(epsi_0) " or " |E| = (d)/(epsi_0)`