A spherical cavity is created in a neutral solid conducting sphere. Inside the cavity, a dipole is placed as shown in the figure. Electrostatic potential at point P only due to charge induced on the inner surface of the cavity is (assume that l << d)

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$\frac{qεsin θ}{4 {πε}_{0} d}$

$\frac{- qℓsin θ}{4 {πε}_{0} d^{2}}$

$- \frac{qℓ}{4 {πε}_{0}} \frac{\sin θ}{d}$

$\frac{qℓ}{4 {πε}_{0}} \frac{\sin θ}{d^{2}}$

answer is B.

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Detailed Solution

If there is any charge inside the cavity of the conductor, the charge induced on the inner surface of the cavity is such that it will produce same amount of electric field but in
opposite direction at each and every point outside the cavity as produced by the charge in the cavity.

The induced charge produces an induced dipole in a direction opposite to the direction of the dipole placed in the cavity

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