Question: Q. 11. An electric dipole of moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. Write the expression for the torque $\vec{\tau}$ experienced by the dipole. Identify two pairs of perpendicular vectors in the expression.
Show diagrammatically the orientation of the dipole in the field for which the torque is (i) the maximum, (ii) half of the maximum value, (iii) zero.
R [O.D. Comptt. I, II, III; 2012, CBSE SQP II; 2009, 08, 07, 06]
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Solution:
Ans. Expression for torque experienced by dipole 1 Identifying two pairs of perpendicular vectors in expression $1 / 2$ Diagrammatic orientation of dipole in field for (i) maximum (ii) half of the maximum value (iii) zero torque
[CBSE Marking Scheme, 2012]
Detailed Answer :
(i) Try yourself, Similar to Question 2(i) Short Answer Type Questions-II
(ii) Try yourself, Similar to Question 9(ii) Short Answer Type Questions-II
(iii) Diagrammatic orientation of dipole in field for (i) maximum (ii) half maximum value (iii) zero torque $\mathbf{1}$
(i) If $\theta$ is $90^{\circ}$, torque will be maximum, and is equal to $p E$ which shows dipole is perpendicular to direction of uniform electric field $E$.
(ii) If $\theta$ is $30^{\circ}$, torque will be $p E \sin \theta$ which is equal to $\frac{p E}{2}$ Since sine $30^{\circ}$ is $\frac{1}{2}$ that shows that torque will be half of the maximum value and dipole will be at $30^{\circ}$ to the direction of uniform electric field $E$.
(iii) If $\theta$ is $0^{\circ}$, torque will be minimum that is equal to 0 since sine $0^{\circ}$ is zero that shows that dipole to be parallel to direction of uniform electric field $E$.
