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The region between two concentric sphere...

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), have volume charge density `rho=A/r`, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

A

`(Q)/(2pi(b^(2)-a^(2)))`

B

`(2Q)/(pi(a^(2)-b^(2)))`

C

`(2Q)/(pia^(2))`

D

`(Q)/(2pia^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`rho=(A)/(r)`
According to gauss.s law
`ointvecE.vec(ds)=(q)/(epsilon_(0))`
`implies Exx4pir^(2)=(Q+int_(a)^(r)(A)/(r)4pir^(2)dr)/(epsilon_(0))`
`implies E=(Q+2piAr^(2)-2piAa^(2))/(4piepsilon_(0)r^(2))`
Make E independent of r
`Q-2piAa^(2)=0`
`implies A=(Q)/(2pia^(2))`.
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