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Deduce the Expression for the Torque Acting on a Dipole of Dipole Moment in the Presence of a Uniform Electric Field - Physics

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Deduce the expression for the torque acting on a dipole of dipole moment `vecp` in the presence of a uniform electric field `vecE`

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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`

Concept: Dipole in a Uniform External Field
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