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Question

A dipole of moment p is placed in uniform electric field E then torque acting on it is given by : -

A
τ=PE
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B
τ=P×E
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C
τ=P+E
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D
τ=PE
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Solution

The correct option is A τ=P×E
Force on charge +q=FA=qE along direction of vector E
Force on charge q=FB=qE opposite to direction of E
As there two forces are equal, they from a couple
Torque(τ)=Force×Armofcoupleτ=F×ABsinθτ=qE×ABsinθτ=qE×2asinθτ=(q×2a)Esinθτ=PEsinθ,wherePindipolemovementτ=P×E

1214805_70892_ans_391d74bd80364dd88c3220c1e58869e6.PNG

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