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Consider the force F on a charge ‘q’ due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if ‘q’ is placed at distance r from the centre of the shell ?

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$F = \frac{1}{4 π \in_{0}} \frac{Q q}{R^{2}} f o r r < R$

$F = \frac{1}{4 π \in_{0}} \frac{Q q}{r^{2}} f o r r > R$

$\frac{1}{4 π \in_{0}} \frac{q Q}{R^{2}} > F > 0 f o r r < R$

$F = \frac{1}{4 π \in_{0}} \frac{Q q}{r^{2}} f o r a l l r$

answer is B.

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Detailed Solution

Electric field inside the charged spherical shell is zero, so force should be zero for r < R.
For outside is $r > R, E = \frac{1}{4 π \in_{o}} \frac{Q}{r^{2}}$ So, $F = \frac{1}{4 π \in_{o}} \frac{Q q}{r^{2}}$

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