Electrostatics Question 706
Question: An electric dipole is placed at an angle of $ 30{}^\circ $ with an electric field of intensity $ 2\times 10^{5}N{{C}^{-1}} $ , it experiences a torque of 4 Nm. Calculate the charge on the dipole if the dipole length is 2 cm.
Options:
A) $ 8mC~~~~ $
B) $ 4mC $
C) $ 8\mu C $
D) $ 2mC $
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Answer:
Correct Answer: D
Solution:
[d] Torque, $ \vec{\tau }=\vec{p}\times \vec{E}=pE\sin \theta $
$ 4=p\times 2\times 10^{5}\times \sin 30{}^\circ $
$ \text{or, }p=\frac{4}{2\times 10^{5}\times \sin 30{}^\circ }=4\times {{10}^{-5}}Cm $ Dipole moment, $ p=q\times l $
$ q=\frac{p}{l}=\frac{4\times {{10}^{-5}}}{0.02}=2\times {{10}^{-3}}C=2mC $
