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There are three concentric thin spheres of radius a, b, c (a > b > c). The total surface charge densities on their surfaces are σ,-σ,σ respectively. The magnitude of electric field at r ( distance from centre) such that a > r > b is

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a

0

b

σε0r2b2-c2

c

σε0r2a2+b2

d

none of these

answer is B.

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Detailed Solution

Electric field at a distance r(a > r > b) will be due to charges enclosed in r only, and since a sphere acts as a point charge for points outside its surface,∴ E=kQcr2+kQbr2=kr2σ×4πc2+(-σ)4πb2 =σε0r2c2-b2

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There are three concentric thin spheres of radius a, b, c (a > b > c). The total surface charge densities on their surfaces are σ,-σ,σ respectively. The magnitude of electric field at r ( distance from centre) such that a > r > b is