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Two identical non-conducting thin hemispherical shells each of radius R are brought in contact to make a complete sphere. If a total charge Q is uniformly distributed on them, how much minimum force F will be required to hold them together?

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$F = \frac{Q^{2}}{16 π ε_{o} R^{2}}$

$F = \frac{Q^{2}}{32 π ε_{o} R^{2}}$

$F = \frac{Q^{2}}{64 π ε_{o} R^{2}}$

$\frac{Q^{2}}{32 π ε_{o} R^{2}} > F > \frac{Q^{2}}{64 π ε_{o} R^{2}}$

answer is B.

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Detailed Solution

Concept of electro static pressure ,

$F = \frac{σ^{2}}{2 ε_{0}} \times$ area of projection.

$= \frac{{(\frac{Q}{4 {πR}^{2}})}^{2}}{2 ε_{0}} \times {πR}^{2} = \frac{Q^{2}}{32 {πε}_{0} R^{2}}$

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