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JEE MAIN 2019
12.04.19_S1
Question
A point dipole $\hat{p}=-p_0 \hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the $y$-axis at a distance $d$ are, respectively: (Take $V=0$ at infinity)
Select the correct option:
A
$\frac{|\vec{p}|}{4 \pi \varepsilon_0 d^2}, \frac{\vec{p}}{4 \pi \varepsilon_0 d^3}$
B
$\frac{|\vec{p}|}{4 \pi \varepsilon_0 d^2}, \frac{-\vec{p}}{4 \pi \varepsilon_0 d^3}$
C
$0, \frac{-\vec{p}}{4 \pi \varepsilon_0 d^3}$
D
$0, \frac{\vec{p}}{4 \pi \varepsilon_0 d^3}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & \vec{E}=K \frac{\vec{p}}{r^3} \sqrt{3 \cos ^2 \theta+1} \\ & \Rightarrow \quad q=p / 2(0, d, 0) \\ & \therefore \quad \vec{E}=\frac{-k \vec{p}}{d^3}\end{aligned}$
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