Let `rho(r) = (Q r)/(piR^4)` be the charge density distribution for a solid sphere of radius R and total charge Q. For a point P inside the sphere at a distance `r_1` from the centre of the sphere, the magnitude of electric field is

Options

A. `Q/(4piepsilon_0r_1^2)`
B. `(Qr_1^2)/(4piepsilon_0R^4)`
C. `(Qr_1^2)/(3piepsilon_0R^4)`
D. zero

Answer

C

Explanation

In figure dotted sphere of radius `r_1` is the Gaussian surface.
According to Gauss.s theorem
`ointvecE.dvecs=q_"inside"/epsilon_0`
`ointE ds cos 0^@=1/epsilon_0 int rho(r) xx dV`
`E(4pir_1^2)xx1=(Qr_1)/(epsilon_0pir^4)xx(4/3pir_1^3)`
`E=(Q. 4pir_1^4)/(3epsilon_0 . piR^4 (4pir_1^2))=(Qr_1^2)/(3piepsilon_0R^4)`