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 equal to $ 4 Nm $ . Calculate the charge on the dipole if the dipole length is $ 2 cm $ .

• A. $ 8\text{ }mC $
• B. $ 4\text{ }mC $
• C. $ 8\mu C $
• D. $ 4\mu C $
• E. $ 2mC $

Answer 1

Answer: (E)

Torque on dipole is $ \tau =pE\sin \theta $
$ \tau =q\times 2lE\sin \theta $
$ \Rightarrow $ $ q=\frac{\tau }{2El\sin \theta } $
Given, $ \tau =4\text{ }Nm,\text{ }E=2\times {{10}^{5}}N{{C}^{-1}}, $
$ l=2\times {{10}^{-2}}m,\theta =30{}^\circ . $
$ \therefore $ $ q=\frac{4}{2\times 2\times {{10}^{5}}\times 2\times {{10}^{-2}}\times \sin 30{}^\circ } $
$ \Rightarrow $ $ q=2mC $