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An electric dipole has a fixed dipole moment $\underset{p}{\rightarrow}$ , which makes angle θ with respect to x-axis. When subjected to an electric field $\underset{E_{1}}{\rightarrow}$ $= E\hat{i}$ it experiences a torque $\underset{T_{1}}{\rightarrow}$ $= \tau \hat{k}$ When subjected to another electric field $\underset{E_{2}}{\rightarrow}$ $= \sqrt{3}E_{1}\hat{j}$ it experiences a torque $\underset{T_{2}}{\rightarrow}$ $= \: -$ $\underset{T_{1}}{\rightarrow}$ The angle θ is :

Option 1)
30⁰

Option 2)
45⁰

Option 3)
60⁰

Option 4)
90⁰

Answers (1)

best_answer

As we have learned

Torque Experienced by the dipole -

$\vec{\tau }=\vec{P}\times \vec{E}$

$\vec{\tau }=PE\sin \Theta$

$\Theta =0^{\circ}$ $\tau =0$

$\Theta =\frac{\pi }{2}$ $\tau = max^{m}$

- wherein

$\vec \tau = \vec P \times \vec E \\ For \: \: \vec E = E \hat i \\ \tau = PE \sin \theta ......(1) \\for \: \: \vec E = \sqrt 3 E \hat j \\ P (\sqrt 3E ) \cos \theta = \tau .....(2)$

Form (1) and (2)

$\tan \theta = \sqrt 3 \\ \theta = 60$

Option 1)

30⁰

Option 2)

45⁰

Option 3)

60⁰

Option 4)

90⁰

Posted by

Avinash

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