Question

The figure shows a non conducting ring which has 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 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 electric field at all points on the axis will be along the axis
• D. If the ring is placed inside a uniform external field then net torque and force acting on the ring would be zero

Answer 1

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

The potential at any axial point of ring is $V=k\frac{Q}{\sqrt{x^2+R^2}}$
As the total charge $\left(Q\right)$ is zero and potential is a scalar quantity. thus the potential at all points on the axis will be zero.
But the electric filed is a vector quantity and here some component of electric field is non zero on the axis and its resultant in direction along perpendicular direction to the axis.
As the electric field is not uniform so net force will not zero. As E is not zero so here torque will not zero.