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Question
Deduce the expression for the torque acting on a dipole of dipole moment `vecp` in the presence of a uniform electric field `vecE`
Solution
Dipole in a Uniform External Field
Consider an electric dipole consisting of charges −q and +q and of length 2a placed in a uniform electric field `vecE`making an angle θ with electric field.
Force on charge `-q" at "A=-qvecE("opposite to" vecE)`
Force on charge `+q" at "B=qvecE("along"vecE)`
Electric dipole is under the action of two equal and unlike parallel forces, which give rise to a torque on the dipole.
τ = Force × Perpendicular distance between the two forces
τ = qE (AN) = qE (2a sin θ)
τ = q(2a) E sinθ
τ = pE sinθ
`:.vect=vecpxxvecE`
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