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A system consits of a uniformly charged ...

A system consits of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density `rho=alpha/r`, where `alpha` is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.

A

`alpha/(2epsilon_(0))`

B

`2/(alphaepsilon_(0))`

C

`2pialphaR^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Using Gauss theorem for spherical surface of radius r outside the sphere with a uniform charge density `rho` and a charge q
`underset(s)intE.ds=(Q_(enc))/(epsi_(0))`
`E4pir^(2)=(1)/(epsi_(0))(q+underset(R)overset(r)int(alpha)/(r)(4pir^(2))dr),`
`E4pir^(2)=((q-2pialphaR^(2)))/(epsi_(0))+(4pialphar^(2))/(2 epsi_(0))`
The intensity E does not depend on R if
`(q-2pialphaR^(2))/(epsi_(0))=0or q=2pialphaR^(2)`
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