JEE Main 2026 — Apr 2, Shift 1 — Physics solution

JEE Main2026Apr 2, Shift 1Physics

Two short electric dipoles $A$ and $B$ having dipole moment $p_{1}$ and $p_{2}$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $6 0^{\circ}$ with the line joining points $O$ and $x$ . The ratio of the dipole moments $p_{2} / p_{1}$ is _______.

A
$\frac{3}{2}$
B
$23$
C
$\frac{1}{3}$
D
$3$

Solution

Point $x$ lies on the axial line of dipole $A$ and on the equatorial line of dipole $B$ . The two contributing fields are perpendicular to each other:

$E_{A} = \frac{2 k p _{1}}{x ^{3}}$ (along the axis, i.e. along $O x$ )

$E_{B} = \frac{k p _{2}}{x ^{3}}$ (perpendicular to $O x$ )

The resultant makes angle $θ$ with $O x$ where $tan θ = E_{B} / E_{A}$ . Setting $θ = 6 0^{\circ}$ :

$tan 6 0^{\circ} = \frac{p _{2}}{2 p _{1}} \Rightarrow 3 = \frac{p _{2}}{2 p _{1}} \Rightarrow \frac{p _{2}}{p _{1}} = 23$

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