Electric Charges and Fields - Result Question 18

18. An electric dipole of moment ’ $p$ ’ is placed in an electric field of intensity ’ $E$ ‘. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $=90^{\circ}$, the torque and the potential energy of the dipole will respectively be :

[2012]

(a) $p E \sin \theta,-p E \cos \theta$

(b) $p E \sin \theta,-2 p E \cos \theta$

(c) $p E \sin \theta, 2 p E \cos \theta$

(d) $p E \cos \theta,-p E \cos \theta$

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Answer:

Correct Answer: 18. (a)

Solution:

  1. (a) The torque on the dipole is given as $\tau=p E \sin \theta$

The potential energy of the dipole in the electric field is given as

$U=-p E \cos \theta$