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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-IList-II
\((P)\)\((1)\)\(\vec{E}=0\)
\((Q)\)\((2)\)\(\vec{E}=-\frac{p}{2 \pi \epsilon_0 \mathrm{r}^3} \hat{\mathrm{j}}\)
\((R)\)\((3)\)\(\vec{E}=-\frac{p}{4 \pi \epsilon_0 \mathrm{r}^3}(\hat{\mathrm{i}}-\hat{\mathrm{j}})\)
\((S)\)\((4)\)\(\vec{E}=\frac{p}{4 \pi \epsilon_0 \mathrm{r}^3}(2 \hat{\mathrm{i}}-\hat{\mathrm{j}})\)
\((5)\)\(\vec{E}=\frac{p}{\pi \epsilon_0 \mathrm{r}^3} \hat{\mathrm{i}}\)

  1. A \(\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4\)
  2. B \(\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 5, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 1\)
  3. C \(\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5\)
  4. D \(\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 5\)
Verified Solution

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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