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Help me answer: - Electrostatics - JEE Main-9

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)
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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

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