Q. A dipole having moment $P$ is placed in front of a solid uncharged conducting sphere as shown in the diagram. The net potential at point $A$ lying on the surface of the sphere is

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A

$\frac{K P c o s \phi}{r^{2}}$

B

$\frac{K P c o s^{2} \phi}{r^{2}}$

C

Zero

D

$\frac{2 K P c o s^{2} \phi}{r^{2}}$

Solution:

Electric potential at center of sphere is $V_{c e n t e r}=$ pot. due to induced charges $+$ pot. due to dipole. but pot. due to induced charges is zero.
$V_{c e n t e r}=\frac{K P}{\left(\right. r s e c \phi \left(\left.\right)^{2}}$
$=\frac{K P c o s^{2} \phi}{r^{2}}$

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