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