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An electric dipole of moment P is placed in front of a grounded sphere as shown in the fig. The charge induced on the surface of the sphere is—
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- Zero
- PR/d2
- PR2/d3
- PR3/d4
Correct Option: B
The charge induced on a spherical surface is given by
– QR/D
where Q is the inducing point charge, D is the distance of the point charge from the centre of the sphere and R the radius of the sphere.
Total charge induced in the present case is
| Q = – qR |  | - |  | ||
| d + d '/2 | d – d '/2 |
| = | = | ||
| d2 – (d '2)/4 | (d '2)/4 |
Now for a dipole d′ is very small, i.e., d′ << d. Hence, Q′ = PR/ d2 where, P = qd′, the dipole moment.
