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A hollow spherical shell of radius r has a uniform charge density $\frac{σ}{π}$ . It is kept in a cube of edge 3r such that the centre of the cube coincides with the centre of the shell. The electric flux that comes out of a face of the cube is

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$\frac{2 r^{2} σ}{3 ε_{0}}$

$\frac{r^{2} σ}{3 ε_{0}}$

$\frac{4 r^{2} σ}{3 ε_{0}}$

$\frac{r^{2} σ}{6 ε_{0}}$

answer is A.

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Detailed Solution

$f l u x f r o m e a c h s u r f a c e o f t h e c u b e i s \frac{Q}{6 ε_{0}} = \frac{4 π r^{2} \frac{σ}{π}}{6 ε_{0}} = \frac{2 r^{2} σ}{3 ε_{0}}$

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