Question

A dipole having dipole moment $P$ is placed in front of a solid neutral conducting sphere as shown in figure. The net potential at a point $A$ on the surface of its sphere is:-

• A. $\frac{kP\cos \varnothing }{r^2}$
• B. $\frac{kP{\cos }^2\varnothing }{r^2}$
• C. $\frac{2kP{\cos }^2\varnothing }{r^2}$
• D. $\frac{kP}{r^2}$

Answer 1

The correct option is B $\frac{kP{\cos }^2\varnothing }{r^2}$

Now$,$ if we want to find the potential at $A,$ then one way is to resolve the dipole$,$ and hence we can say that potential is

$V_A=\frac{kP\cos \varphi }{r^2}$

however$,$ if we notice that $V_A=V_o$

Since $V_{induced}=0,$ we can say that

$V_o=\frac{kP{\cos }^2\varphi }{r^2}$

$\Rightarrow V_A=V_o=\frac{kP{\cos }^2\varphi }{r^2}$

Hence,

option $\left(B\right)$ is correct answer.