Question

An ideal dipole of dipole moment $\overrightarrow{p}$ is placed in front of an uncharged conducting sphere of radius R as shown :

• A. The potential at point A is $\frac{KP}{(r-R{)}^2}$
• B. The potential at point A is $\frac{KP}{r^2}$
• C. The potential due to dipole at point B is $\frac{KP}{(r+R{)}^2}$
• D. The potential due to dipole at point B is $\frac{KP}{r^2}$

Answer 1

The correct option is B The potential at point A is $\frac{KP}{r^2}$

As for conductors, potential at surface is equal to the potential inside the conductor. So, $V_A=V_O$

Now $V_O=$ potential at O due to dipole + potential at O due to sphere

Thus, $V_O=\frac{KP}{r^2}+0$ (as the conductor is uncharged)

$⟹V_A=V_O=\frac{KP}{r^2}$