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Obtain the Expression for the Torque τ Experienced by an Electric Dipole of Dipole Moment P in a Uniform Electric Field, E . - Physics

(i)Obtain the expression for the torque `vecτ` experienced by an electric dipole of dipole moment `vecP` in a uniform electric field, `vecE` .

(ii) What will happen if the field were not uniform?

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(i) Consider an electric dipole consisting of charges −q and +q and of length 2a placed in a uniform electric field making an angle θ with electric field.

Force on charge −q at `A=-qvecE`(opposite to`vecE`)

Force on charge +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 (2sin θ)

τ = q(2aE sinθ

τ = pE sinθ

`therefore vectau=vecPxxvecE`

(ii) If the electric field in not uniform then both the charges of the dipole will experience a different force (not equal and opposite) at slightly different positions in the field and hence a net force acts on the dipole in a nonuniform electric field. Also, a net torque acts on the dipole which depends on the location of the dipole in the nonuniform electric field. 

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