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Question

A cavity is made inside a solid conducting sphere and a charge q is placed inside the cavity at the centre. A charge q1 is placed outside the sphere, as shown in the figure. Point A is inside the sphere and point B is inside the cavity. Then


A
Electric field at point A is zero.
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B
Electric field at point B is 14πϵoqy2.
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C
Potential at point A is 14πϵo[q1a+qR].
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D
Potential at point B is 14πϵo[q1a+qR+qyqr]
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Solution

The correct option is D Potential at point B is 14πϵo[q1a+qR+qyqr]
The charge distribution is shown in figure.
Due to q1, the charge induction is non-uniform, but the net induced charge due to q1 is zero.

At point A, the electric field is zero.

At point B, the electric field is due to charge q only.
EB=14πϵoqy2

At point A, potential is equal to the potential at centre.

VA=Vcentre=14πϵoqR+14πϵoq1a=14πϵo[q1a+qR]

At point B, potential is due to charges, q at centre of cavity, q induced on inner surface of cavity, in addition to the potential at the centre.
VB=14πϵo[q1a+qR+qyqr]

Therefore, all the options are correct.

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