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A positive charge is distributed in a sp...

A positive charge is distributed in a spherical region with charge density `rho=rho_(0) r` for `r le R` (where `rho_(0)` is a positive constant and r is the distance from centre). Find out electric potential and electric field at following loations.
(a) At a distance r from centre inside the sphere. (b) At a distance r from centre outside the sphere.

Text Solution

Verified by Experts

The correct Answer is:
`0, (2Klambda)/r, 0`
(i) `q=int dq=underset(0)overset(R)(int) rho_(0) r/Rxx4pi r^r=(rho_(0)x4pi R^(4))/R=pi rho_(0)R^(3)`
(ii) `E=(KQ')/r^(2)=K/r^(2)xx(rho_(0)pir^(4))/R=(KQr^(2))/R^(4)` where
`Q'=underset(0)overset(tau)(int)rho_(0)x/Rxx4pix^(2)dx=rho_(0)/(4R)xx4pixxr^(4)=(rho_(0)pi r^(4))/R`
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