Question

# An electric dipole of moment $$\mu$$ of $$400\mu C\ m$$ is placed in a transverse electric field $$(E)$$ of $$50\ Vm^{-1}$$ at an angle of $$30^{\circ}$$ to $$E$$. Then, a torque of

A
102Nm acts along the direction E
B
102Nm acts normal to both E and μ
C
105Nm acts normal to both E and μ
D
103Nm acts along the direction E
E
None of these

Solution

## The correct option is C $$10^{-2}Nm$$ acts normal to both $$E$$ and $$\mu$$Given, $$P = 400\mu C = 400\times 10^{-6}C$$$$E = 50\ Vm^{-1}$$$$\theta = 30^{\circ}$$We know that, torque acting on an electric dipole, $$\tau = PE\sin \theta$$where, $$P =$$ dipole moment$$= 400\times 10^{-6}\times 50\times \sin 30^{\circ}$$$$= 400\times 10^{-6} \times 50 \times \dfrac {1}{2}$$$$= 200\times 50\times 10^{-6} = 10^{-2} N-m$$This torque will act normal to both $$E$$ and $$\mu$$.Physics

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