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 in_(0) r_(1)^(2))`
B. `(Q r_(1)^(2))/(4pi in_(0)R^(4))`
C. `(Q r_(1)^(2))/(3n pi in_(0) R^(4))`
D. zero

Answer

C

Explanation

In Fig, dotted sphere of radius `r_(1)` is the Gaussaian surface.According to Gauss's theroem,

`oint vec(E).d vec(s) = (q_(inside))/(in_(0))`
`E ds cos 0^(@) = (1)/(in_(0)) rho (r ) xx dV`
`E (4pi r_(1)^(2)) xx1 = (Q r_(1))/(in_(0) pi R^(4)) ((4)/(3) pi r_(1)^(3))`
`E = (Q. 4 pi r_(1)^(4))/(3in_(0) pi R^(4) (4pi r_(1)^(2))) = (Q r_(1)^(2))/(3pi in_(0) R^(4))`