Two short electric dipoles A and B having dipole moment and respectively are placed with their axis mutually perpendicular as shown in the figure

Question

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 $60 °$ with the line joining points $O$ and $x$ . The ratio of the dipole moments $\frac{P_{2}}{P_{1}}$ is ________ . [2026]

Smart Achievers · Accepted Answer

(2)

${\vec{E}}_{A} = \frac{2 k P_{1}}{x^{3}} (\hat{i})$ ${Axial point}$

${\vec{E}}_{B} = \frac{k P_{2}}{x^{3}} (\hat{j})$ ${Equatorial point}$

$Now \tan θ = \frac{| {\vec{E}}_{B} |}{| {\vec{E}}_{A} |}$

$\tan 60 ° = \frac{\frac{k P_{2}}{r^{3}}}{\frac{2 k P_{1}}{r^{3}}} = \frac{P_{2}}{2 P_{1}} = \sqrt{3}$

$\Rightarrow \frac{P_{2}}{P_{1}} = 2 \sqrt{3}$

Solution

1 $\frac{\sqrt{3}}{2}$

2 $2 \sqrt{3}$

3 $\frac{1}{\sqrt{3}}$

4 $\sqrt{3}$

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Solution

1 32

2 23

3 13

4 3

Ans. (2) E→A=2kP1x3 (i^) {Axial point} E→B=kP2x3 (j^) {Equatorial point} Now tanθ=|E→B||E→A| tan60°=kP2r32kP1r3=P22P1=3 ⇒P2P1=23

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1 $\frac{\sqrt{3}}{2}$

2 $2 \sqrt{3}$

3 $\frac{1}{\sqrt{3}}$

4 $\sqrt{3}$