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Question
An electric dipole of length 2 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of \[8\sqrt{3}\] Nm. Calculate the potential energy of the dipole, if it has a charge \[\pm\] 4 nC.
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Solution
Torque, \[\tau = \text { PE sin }\theta = \left( Ql \right)\text { E sin }\theta\] ........ (1)
Here, l is the length of the dipole, Q is the charge and E is the electric field.
Potential energy,
\[\text { U = - P Ecos }\theta = - \left( Ql \right)\text {Ecos}\theta\]
Dividing (2) by (1):
\[\frac{\tau}{U} = \frac{\left( Ql \right)E\sin\theta}{- \left( Ql \right)E\cos\theta} = - \tan\theta\]
\[ \Rightarrow U = - \frac{\tau}{\tan\theta}\]
\[ \Rightarrow U = - \frac{\tau}{\tan {60}^o}\]
\[ \Rightarrow U = - \frac{8\sqrt{3}}{\sqrt{3}}\]
\[ \Rightarrow U = - 8 J\]
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