Two hemispherical thin shells made of insulating materials are concentrically arranged in free space as shown. The radii of the larger and the smaller hemispheres are R and r and they carry net positive charges Q and q respectively. The charges are uniformly distributed over the surfaces of the shells. Find the force of electrostatic interaction between the shells. (Given : Electric intensity due to a uniformly charged spherical thin shell is zero anywhere inside it and for external point, the charge on shell behaves like a point charge at the centre of the shell)

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$I n c a s e (a) F = \frac{Q q}{16 π ε_{0} R^{2}}$

$I n c a s e (b) F = \frac{Q q}{16 π ε_{0} R^{2}}$

$I n c a s e (a) F = \frac{Q q}{8 π ε_{0} R^{2}}$

$I n c a s e (b) F = \frac{Q q}{8 π ε_{0} R^{2}}$

answer is A, C.

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Detailed Solution

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F on C is zero. Which means both the hemispheres a and b exert equal force on.
So
$F_{a c} = F_{b c} = F (s a y)$

Force by a on hemispheres c and d are equal
Which means $2 F = 2 q \frac{σ}{4 ε_{0}}$
$σ = \frac{Q}{2 π R^{2}}$
$F = \frac{Q q}{4 π ε_{0} R^{2}}$