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The region between two concentric sphere...

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has 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

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`Q + int_(a)^( r) s dr =q`
where `rho =A/r^(2), S = 4pir^(2)`

`Q + int_(a)^(r ) 4pir dr = epsilon_(0) [therefore phi =E_(S)]`
`therefore phi + (4piAr^(2))/2 -(4piAa^(2))/2 = E xx 4pir^(2)epsilon(0)`
E is constant in between the spheres. So that it is independent of r.
`therefore phi - 2piAa^(2) =0`
`therefore A = Q/(2pia^(2))`
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