Q 12-02-051JEE MainJEE Main 2025 (22 Jan, Shift 2)Medium
For a short dipole placed at origin $O$, the dipole moment $P$ is along the $x$-axis, as shown in the figure. If the electric potential and electric field at $A$ are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point $B$ on the $y$-axis is given by
Answer: (B) zero and $\dfrac{E_0}{16}$
$A$ is on the axis at distance $r$: $E_0 = \dfrac{2kp}{r^3}$.
$B$ is on the equatorial line (the $y$-axis) at distance $2r$:
- Potential on the equatorial line of a dipole is zero: $V_B = 0$.
- Field: $E_B = \dfrac{kp}{(2r)^3} = \dfrac{kp}{8r^3} = \dfrac{1}{16}\cdot\dfrac{2kp}{r^3} = \dfrac{E_0}{16}$.
Solution by Sreeraj P, M.Sc Physics