Question: Q. 10. An electric dipole is placed in a uniform electric field.

(i) Show that no translatory force acts on it.

(ii) Derive an expression for the torque acting on it.

(iii) Find work done in rotating the dipole through 180.

A [Delhi Comptt. I, II, III, 2014,

O.D. I, II, III, 2013, 2012]

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Solution:

Ans. Electric dipole of charges +q and q separated by distance 2a is shown in the figure.

It is placed in a uniform electric field at an angle θ with it.

(i) Force on charge +q,F1=qE, in the direction of E.

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Force on charge q,F2=qE, in the opposite

direction of E.

Net translatory force on dipole $=\vec{F}{1}+\overrightarrow{F{2}}$

=+qEqE=0

Hence, no translatory force acts on it.

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(ii) But the two equal, parallel and unlike forces form a couple in which a torque is given by

τ= Force × perpendicular distance   between the two forces 

where, p=q×2a= dipole moment

(iii) Work done in rotating the dipole through 180 is

W=d W  W=0180τdθ=pE0180sinθdθ W=pE[cosθ]0180 W=pE[cos180cos0] W=pE[1+1]=2pE



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