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Let P(r)=(Q)/(piR^4)r be the charge dens...

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:

A

0

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
c
Charge density , `rho=(Q)/(piR^(4))r`,
The electric field at the point P distant `r_(1)` from the centre , according to Gussa .s theorem is
`E*4pir_(1)^(2)=` charge enclosed `d//epsilin_(0)`
`E*4pir_(1)^(2)=(1)/(epsilon_(0))intrhodV=(1)/(epsilon_(0))int_(0)^(r_(1))(Qr)/(piR^(4))*4pir^(2)dr`
`rArrE=(Qr_(1)^(2))/(4piepsilon_(0)R^(4))`
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