Question

Statement (1) : For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on the axis of the ring is zero.
Statement (2) : For a non-uniformly charged thin circular ring with net charges as zero, electric field at any point on the axis of the ring is zero.

• A. $\left(1\right)$ is true, $\left(2\right)$ is false.
• B. $\left(1\right)$ is false, $\left(2\right)$ is true.
• C. Both statements are true.
• D. Both statements are false.
  

Answer 1

The correct option is A $\left(1\right)$ is true, $\left(2\right)$ is false.

The electric potential of uniformly charged ring of radius $R$ at axial distance $x$ from the ring is given by.
$V=\frac{kQ}{\sqrt{x^2+R^2}}$
$V=0$ if $Q=0$
Hence, statement $\left(1\right)$ is correct.

However, electric field $E$ is a vector quantity and the field is resultant effect of all the charges, so it may have some non-zero component on the axis of the ring.

$E\ne 0$

So option $\left(a\right)$ is correct.