Home
Class 12
PHYSICS
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/(4 pi _0r_1^2)`

C

`(Qr_1^2)/(4 pi varepsilon_0R_4)`

D

`(Qr_1^2)/(3 pi varepsilon_0R_4)`

Text Solution

Verified by Experts

The correct Answer is:
C
Consider a spherical shell having radius `r` and thickness dr
`dq = Q/(pi R^4) r xx 4 pi r^2 dr`
or `q = (4 Q)/( R^4 int)^(rt) r^3 dr`

so ` vr% , q = (Qr_1^4)/R^4`
Electric field at a distance (r _1) from the center (inside )
`E = 1/(4 pi varepsilon_0 ). q/(r_1^2`
`E = 1/(4 pi varepsilon_0) xx (Qr_1^2)/(R^4)` .
Promotional Banner

Similar Questions

Explore conceptually related problems

A hallow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:

Let p=(Qr^(3))/(piR^(5)) be the volume charge density at distance r from the centre for a a soild sphere of radius R and charge Q. The electric field at r= (R)/(2) from the centre will be

A sphere of radius R has a charge density sigma . The electric intensity at a point at a distance r from its centre is

A conducting sphere of radius R is charged to a potential of V volts. Then the electric field at a distance r ( gt R) from the centre of the sphere would be