JEE MAIN - Physics (2025 - 22nd January Evening Shift - No. 13)
For a short dipole placed at origin O , the dipole moment P is along $x$-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
_22nd_January_Evening_Shift_en_13_1.png)
$\frac{V_0}{2}$ and $\frac{E_0}{16}$
zero and $\frac{E_0}{8}$
$\mathrm{V}_0$ and $\frac{\mathrm{E}_0}{4}$
zero and $\frac{E_0}{16}$
Explanation
$$\begin{aligned}
& E_A=\frac{2 k P}{r^3}=E_0 \& V_A=\frac{k P}{r^2}=v_0 \\
& E_B=\frac{k P}{(2 r)^3}=\frac{E_0}{16} \& V_B=\frac{k \vec{p} \cdot \hat{r}}{r^2}=0
\end{aligned}$$
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