SATHEE: electric-charges-and-fields Question 14

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Question: Q. 4. An electric dipole is placed in a uniform electric

field $\vec{E}$ with its dipole moment $\vec{p}$ parallel to the field. Find

(i) the work done in turning the dipole till its dipole moment points in the direction opposite to $\vec{E}$ .

(ii) the orientation of the dipole for which the torque acting on it becomes maximum.

A [Comptt. O.D. I, II, III 2014]

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Solution:

Ans. (i) We have $W = \int_{θ_{1}}^{θ_{2}} τ d θ$

$∴ W = \int_{0}^{π} p E \sin θ d θ$

$W = p E [- \cos θ]_{0}^{π}$

$W = - 2 p E$

$τ = p E \sin θ$

(ii) For $θ = \frac{π}{2}, τ$ is maximum.

[CBSE Marking Scheme, 2014]

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