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Consider a uniformly charged spherical surface with charge per unit surface area $σ$ . A small patch of small area dA is removed from it to create a hole (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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Field at locality of hole $= \frac{σ}{2 ε_{0}}$

Field at locality of hole $= \frac{σ}{ε_{0}}$

If now we try to put the patch to close the hole it experiences an outward force of $\frac{σ^{2}}{2 ε_{0}} (d A)$

If now we try to put the patch to close the hole it experiences an outward force of $\frac{σ^{2}}{ε_{0}} (d A)$

answer is A, C.

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Detailed Solution

$E_{1} + E_{2} = \frac{K Q}{R^{2}} = \frac{σ}{ε_{0}} E_{1} + E_{2} = 0 ∴ E_{1} = E_{2} = \frac{σ}{2 ε_{0}}$

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