Question

Mark the incorrect statement(s), (Assume reference point to be at infinity)

• A. Electric potential at the centre of a uniformly charged spherical shell due to its own charge is zero.
• B. Electric potential at the centre of a uniformly charged sphere due to its own charge is zero.
• C. Self energy of a dipole is positive.
• D. If we change the reference point, the potential difference between 2 points will not change.

Answer 1

Answer: (A), (B), (C)

Self energy of a dipole is positive.

In case of spherical shell, we select a gaussian surface concentric with the shell of radius $r(r>R)$.
So, $\oint \overrightarrow{E}.\overrightarrow{ds}=E\left(4\pi r^2\right)\cos 0$

According to Gauss law,
$E\left(4\pi r^2\right)\cos 0=\frac{Q_{encl}}{{ϵ}_o}$​​

Since charge enclosed inside the spherical shell is zero.
So, $E=0$, but $V$ is not zero.

For a shell,
$V_{center}=V_{surface}=\frac{kQ}{R}$
For a sphere,
$V_{center}=\frac{3kQ}{2R}$

Self energy of a dipole is negative since self energy is the total binding energy.