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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$\frac{σ}{ε_{0} r^{2}} (a^{2} + b^{2})$

$\frac{σ}{ε_{0} r^{2}} (b^{2} - c^{2})$

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,

$∴ E = \frac{{kQ}_{c}}{r^{2}} + \frac{{kQ}_{b}}{r^{2}} = \frac{k}{r^{2}} (σ \times 4 {πc}^{2} + (- σ) 4 {πb}^{2}) = \frac{σ}{ε_{0} r^{2}} (c^{2} - b^{2})$