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A spherical space of radius R is uniformly charged and electric flux through the surface of this spherical space is $ϕ$ . What will be the electric field at a point on the surface of a concentric spherical space of radius $\frac{R}{2}$ ?

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$ϕ / 8 π R^{2}$

$\frac{\in_{0} ϕ}{4 π R^{2}}$

$\frac{ϕ}{2 π R^{2}}$

$\frac{ϕ}{4 π R^{2}}$

answer is B.

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Detailed Solution

If Q be the net charge enclosed by surface (1), then $Q = \in_{0} ϕ$

$Q^{1} =$ Net charge enclosed by surface - (2).

$= \frac{Q}{\frac{4}{3} π R^{3}} \times \frac{4}{3} π {(\frac{R}{2})}^{3} = \frac{Q}{8} = \frac{\in_{0} ϕ}{8}$

$∴ E_{P} = \frac{1}{4 π \in_{0}} \frac{Q^{1}}{{(\frac{R}{2})}^{2}} = \frac{Q'}{4 π \in_{0}} \frac{4}{R^{2}} = \frac{ϕ}{8 π R^{2}}$

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