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A sphere of charges of radius R carries a positive charge whose volume chasrge density depends only on the distance r from the ball's centre as `rho=rho_0(1-r/R),` where `rho_0` is constant. Assume epsilon as theh permittivity of space.
The magnitude of electric field as a function of the distance r inside the sphere is given by

A

`E=(p_(0)R^(3))/(8epsilonx^(2))`

B

`E=(p_(0)R^(3))/(12epsilonx^(2))`

C

`E=(p_(0)R^(2))/(8epsilonx^(2))`

D

`E=(p_(0)R^(2))/(12epsilonx^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
For outside the ball
`E=(qtotal)/(4 pi e_0 r^2)`…….(iii) where `q_(total) =int_0^R (4 pi r^2) (p_0) (1-r/R)dr`
Substituting this value in Eq. (ii), we get , `E=(p_0R^3)/(12er^2)`
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