Let `P(r)=(Q)/(piR^4)r` be the charge density 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. `Q/(4pi epsilon_(0)r_(1)^(2))`
B. `(Qr_(1)^(2))/(4pi epsilon_(0)R^(4))`
C. `(Qr_(1)^(2))/(3pi epsilon_(0)R^(4))`
D. Zero

Answer

C

Explanation

In the figure dotter sphere of radius `r_(1)` is the Gaussian surface.
According to gauss.s theorem
`oint vecE.vec(ds)=("q inside")/(epsilon_(0))`

`Eds cos 0^(@)=1/( epsilon_(0)) p (r) xxdV`
`E(4pi r_(1)^(2))xx1=(Qr_(1))/(epsilon_(0)R^(4))xx(4/3 pir_(1)^(3))`
`E=(Q.4pir_(1)^(4))/(3 epsilon_(0). piR^(4)(4pir_(1)^(2)))=(Qr_(1)^(2))/(3pi epsilon_(0)R^(4))`