JEE Advanced · Physics · 17. Electrostatics
List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude \(p\), oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance \(2 r\) apart along the \(x\) direction. The midpoint of the line joining the two dipoles is \(X\). The possible resultant electric fields \(\vec{E}\) at \(X\) are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.
| List-I | List-II | ||
|---|---|---|---|
| \((P)\) | ![]() | \((1)\) | \(\vec{E}=0\) |
| \((Q)\) | ![]() | \((2)\) | \(\vec{E}=-\frac{p}{2 \pi \epsilon_0 \mathrm{r}^3} \hat{\mathrm{j}}\) |
| \((R)\) | ![]() | \((3)\) | \(\vec{E}=-\frac{p}{4 \pi \epsilon_0 \mathrm{r}^3}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\) |
| \((S)\) | ![]() | \((4)\) | \(\vec{E}=\frac{p}{4 \pi \epsilon_0 \mathrm{r}^3}(2 \hat{\mathrm{i}}-\hat{\mathrm{j}})\) |
| \((5)\) | \(\vec{E}=\frac{p}{\pi \epsilon_0 \mathrm{r}^3} \hat{\mathrm{i}}\) |
- A \(\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4\)
- B \(\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 5, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 1\)
- C \(\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5\)
- D \(\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 5\)
Answer & Solution
Correct Answer
(C) \(\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5\)
Step-by-step Solution
Detailed explanation

\(E_{\text {net }}=\frac{-2 k P}{r^3} \hat{j}\)
\(E_{n e t}=\frac{-P \hat{j}}{2 \pi \epsilon_0 r^3}\)

\(\mathrm{E}_{\mathrm{net}}=0\)

\(\frac{2 \mathrm{P} \hat{\mathrm{i}}}{4 \pi \epsilon_0 \mathrm{r}^3}-\frac{\mathrm{P} \hat{\mathrm{j}}}{4 \pi \epsilon_0 \mathrm{r}^3}\)

\(\mathrm{E}_{\mathrm{net}}=\frac{4 \mathrm{kP} \hat{\mathrm{i}}}{\mathrm{r}^3}\)
\(\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5\)
Ans. (C)
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