Question

A dipole having dipole 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 :

• A. $\frac{kp\cos \varphi }{r^2}$
• B. $\frac{ko{\cos }^2\varphi }{r^2}$
• C. $Zero$
• D. $\frac{2kp{\cos }^2\varphi }{r^2}$

Answer 1

The correct option is B $\frac{ko{\cos }^2\varphi }{r^2}$

: If we want to find potential at $A$

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

$V_A=V_0\to$

$V_0=V_{ind.}+V_{dipol.};$

$V_{ind=0}$

$V_0=\frac{K_p{\cos }^2\varphi }{r^2};$

$V_A=V_0=\frac{K_p{\cos }^2\varphi }{r^2}$