Question

The figure shows a non-conducting ring with positive and negative charge non uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

• A. The potential at all the points on the axis will be zero.
• B. The electric field at all the points on the axis will be zero.
• C. The direction of the electric field at all points on the axis will be along the axis
• D. If the ring is placed inside a uniform external electric field, then net torque and force acting on the ring would be zero.

Answer 1

The correct option is A The potential at all the points on the axis will be zero.

The pontential at any axial point of the ring is
$V=\frac{kQ}{\sqrt{x^2+R^2}}$
As the total charge $\left(Q\right)$ is zero and we know that potential is a scalar quantity. Thus the potential at all points on the axis will be zero.
But the electric field is a vector quantity. Here, some electric field component is non zero on the axis and its resultant is in direction along perpendicular direction to the axis.

There will be net torque on the ring.