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Let rho(r)=(Qr)/(piR^(4)) be the charge ...

Let `rho(r)=(Qr)/(piR^(4))` be the charge density distribution for a soild 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

A

`Q/(4piepsilon_(0)r_(1)^(2))`

B

`(Qr_(1)^(2))/(4piepsilon_(0)R^(4))`

C

`(Qr_(1)^(2))/(3piepsilon_(0)R^(4))`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
B
In figure dotted sphere of radius `r_(1)` is the Gaussian surface.
According to Gauss's theorem
`ointvecE.d vecs=(q _("inside"))/(epsi_(0))`
`ointE ds cos 0^(@)=(1)/(epsi_(0))ointrho(r)dV`
`E(4pir_(1))^(2)=(Q)/(epsi_(0)piR^(4))underset(0)overset(r_(1))intr(4pir^(2))dr`
`=(4Q)/(epsi_(0)R^(4))((r_(1)^(4))/(4))=(Q)/(epsi_(0))((r_(1))/(R))^(4)`
`therefore E=(Q)/(4piepsi_(0))(r_(1)^(2))/(R^(4))`
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