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

Answer

A

Explanation

`Q'=int rhodV=underset(0)overset(r_(1))(int)Q/(pi R^(4))r. (4pir^(2))dr=(4Q)/R^(4)[r_(1)^(4)/4]`
`E=(KQ')/r_(1)^(2)=1/(4pi in_(0) r_(1)^(2))[(4Qr_(1)^(4))/(4R^(4))]=(Qr_(1)^(2))/(4pi in_(0) R^(4))`