JEE Main 2025 — Electrostatics Question with Solution

Electric potential and field at point A:

At point A (on the $x$-axis), the electric field is $E_A=\frac{2kP}{r^3}=E_0$ and the potential is $V_A=\frac{kP}{r^2}=V_0$.

Electric potential and field at point B:

Point B is on the $y$-axis, which is at the same distance from the origin as point A, but in a direction perpendicular to the dipole moment.

The field at point B is given by $E_B=\frac{kP}{(2r{)}^3}=\frac{E_0}{16}$. This is because the distance from O to B is $2r$, and the formula for the field off the axis (on the equatorial line) is used.

The potential at point B is $V_B=\frac{k\vec{p}\cdot \hat{r}}{(2r{)}^2}=0$, since $\vec{p}$ and $\hat{r}$ are perpendicular at B, so their dot product is zero.