JEE Advanced 2025 — Paper 1 — PHY-IV solution

JEE Advanced2025Paper 1PHY-IV

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 $E$ 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.

A
P $\to$ 3; Q $\to$ 1; R $\to$ 2; S $\to$ 4
B
P $\to$ 4; Q $\to$ 5; R $\to$ 3; S $\to$ 1
C
P $\to$ 2; Q $\to$ 1; R $\to$ 4; S $\to$ 5
D
P $\to$ 2; Q $\to$ 1; R $\to$ 3; S $\to$ 5

Solution

The field of an ideal dipole on its equatorial plane is $- \frac{k p}{r ^{3}}$ , and on its axis is $+ \frac{2 k p}{r ^{3}}$ , with $k = \frac{1}{4 π ϵ _{0}}$ .

(P) Both dipoles point along $+ \hat{j}$ and $X$ lies on their equatorial planes. Each contributes $- \frac{k p}{r ^{3}} \hat{j}$ , summing to $E = - \frac{2 k p}{r ^{3}} \hat{j} = - \frac{p}{2 π ϵ _{0} r ^{3}} \hat{j}$ . Matches (2).

(Q) The two equatorial contributions are equal and opposite (one up, one down), so $E = 0$ . Matches (1).

(R) The left dipole ( $+ \hat{j}$ , equatorial point) gives $- \frac{k p}{r ^{3}} \hat{j}$ . The right dipole ( $+ \hat{i}$ , axial point) gives $+ \frac{2 k p}{r ^{3}} \hat{i}$ . Total: $E = \frac{p}{4 π ϵ _{0} r ^{3}} (2 \hat{i} - \hat{j})$ . Matches (4).

(S) Both dipoles point along $+ \hat{i}$ and $X$ sits on the axis of each. Each gives $+ \frac{2 k p}{r ^{3}} \hat{i}$ , summing to $E = \frac{4 k p}{r ^{3}} \hat{i} = \frac{p}{π ϵ _{0} r ^{3}} \hat{i}$ . Matches (5).

$∴$ P $\to$ 2, Q $\to$ 1, R $\to$ 4, S $\to$ 5. Option (C).

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