The electric field in the region between two concentric charged spherical shells
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Let us find total charge enclosed in a sphere of radius r,
Q
′
=Q+∫
a
r
r
A
4πr
2
dr=Q+2πAr
2
−2πAa
2
By Gauss law,
E×4πr
2
=Q−2πAa
2
+2πAr
2
Given, E is independent of r
Hence, Q−2πAa
2
=0
This gives A=
2πa
2
Q
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