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Q.

A dipole of dipole moment p is placed at a distance 2R from the centre of a neutral conducting sphere of radius R. The direction of dipole is towards the centre of the sphere. A tangent is drawn from the dipole to the sphere which meets the sphere at point A. Mark the correct option.

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a

The potential at point A is p/16πε0R2

b

The potential at point A is 3p/24πε0R2

c

The potential at point A due to induced charges is (3+23)p/48πε0R2

d

The potential at point A due to dipole is 3p/4πε0R2

answer is A.

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Detailed Solution

Potential at center and at any point on the sphere will be sameSo,VA=VC=P4π∈0(2R)2=P16π∈0R2----(1)(VA)dipole=Pcos30o4π∈0(R3)2∵r=R3 and θ=30°(VA)Dipole=3 P24π∈0R2------(2)potential due to induced charges =(VA)In=VA−(VA)Dipole (VA)In=P(3−23)48π∈0R2 from (1) and (2)

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