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

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

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

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

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

answer is B.

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Detailed Solution

$E = \frac{1}{4 π ε_{0}} (\frac{q_{b} + q_{c}}{r^{2}}) = \frac{1}{4 π ε_{0}} (\frac{- σ \times 4 π b^{2} + σ \times 4 π c^{2}}{r^{2}}) = \frac{σ \times 4 π}{4 π ε_{0}} (\frac{- b^{2} + c^{2}}{r^{2}})$

Where $q_{b} = - σ \times 4 π b^{2}$

$q_{c} = σ \times 4 π c^{2}$ .

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