electric-charges-and-fields Question 17

Question: Q. 7. An electric dipole is held in a uniform electric field.

(i) Show that the net force acting on it is zero.

(ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle of 180.

R [O.D. I, II, III 2012]

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Solution:

Ans. (i)

$$ \begin{aligned} & \vec{F}{\text {net }}=\vec{F}{1}+\vec{F}{2} \ \therefore \quad & \vec{F}{\text {net }}=\overrightarrow{0} \end{aligned} $$

(ii)

W=Ep(cosθ1cosθ2)1/2 W=2Ep1/2

[CBSE Marking Scheme, 2012]

Detailed Answer :

(i) In an electric dipole with two equal and opposite point charges, q at point A and +q at point B with distance 2a as shown, so AB=2a with dipole moment |P|=q(2a)

If dipole is kept in an uniform external electric field E at angle θ with direction of E, then :

(a) force on charge q at point A=qE, opposite to E (b) force on charge +q at point B=+qE, along E

Hence, net force on dipole will be given as:

qEqE=0

(ii) Work done,

W=Ep(1cosθ) =Ep(1cos180) =2Ep joules 

or

Work done on dipole, W=ΔU

(1)=pE(cosθ1cosθ2) W=pE(cos0cos180) W=2pE



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