Let `P(r) = (Q)/(pi R^(4)) r` be the charge desntiy distribution for a solid sphere of radius R and total charge Q. for a point 'p' inside the sphere at distance `r_(1)` from the centre of the sphere, the magnitude of electric field is

Options

A. Zero
B. `Q/(4pi epsilon_0r_1^2)`
C. `(Qr_1^2)/(4pi epsilon_0R^4)`
D. `(Qr_1^2)/(3pi epsilon_0R^4)`

Answer

C

Explanation

`E4 pi r_1^2= (int_0^(r_1) Q/(pi R^4) r4 pi r^2 dr)/e_0 implies E=(Qr_1^2)/(4 pi e_0 R^4)`