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Question

An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle 0 with the direction of the field. Assuming that the potential energy of the dipole to be zero when $$\theta = 90^0$$, the torque and the potential energy of the dipole will respectively be:


A
pEsinθ,2pEcosθ
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B
pEcosθ,pEsinθ
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C
pEsinθ,pEcosθ
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D
pEsinθ,2pEcosθ
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Solution

The correct option is C $$pE \, sin \theta,  - pE\, cos \,\theta $$

Potential energy of the dipole
$$U=-\int { T } dB$$
    $$=-\int _{ \pi /2 }^{ \theta  }{ PE\sin\theta  } d\theta $$
    $$=PE\left( \cos\theta -0 \right) =-PE\cos\theta $$
and potential energy $$=PE\sin\theta $$.

1238536_1138175_ans_d85c79a280df48edbd535269bea686bb.jpg

Physics

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