1. The answer is (A).

The force on the test charge is zero because the ring is a symmetrical object and the test charge is placed at its center. The force from each side of the ring is equal in magnitude and opposite in direction, so they cancel out.

  1. The answer is (B).

The force of interaction between two charges is inversely proportional to the square of the distance between them. So, if the distance between them is reduced to half, the force of interaction will be quadrupled.

  1. The answer is $\frac{r}{2}$.

The electric potential is zero at a point where the electric field is zero. The electric field is zero at the midpoint between two charges of equal magnitude and opposite sign.