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Torque on a Dipole. An electric dipole with dipole moment

Chapter 21, Problem 59E

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QUESTION:

Torque on a Dipole. An electric dipole with dipole moment is in a uniform external electric field (a) Find the orientations of the dipole for which the torque on the dipole is zero. (b) Which of the orientations in part (a) is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.) (c) Show that for the stable orientation in part (b), the dipole’s own electric field tends to oppose the external field.

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QUESTION:

Torque on a Dipole. An electric dipole with dipole moment is in a uniform external electric field (a) Find the orientations of the dipole for which the torque on the dipole is zero. (b) Which of the orientations in part (a) is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.) (c) Show that for the stable orientation in part (b), the dipole’s own electric field tends to oppose the external field.

ANSWER:

Solution 59E Introduction Af first we have to calculate the orientation of the dipole with respect to the electric field where the torque will be zero. Then we have to find out which one of them is the stable orientation and which one is unstable. And finally we have to show that the field created by the dipole at the stable orientation opposes the initial electric field. Step 1: (a) The torque on an electric dipole in uniform electric field is given by Where is the unit vector perpendicular to the plane containing and . Now if torque is zero we must have So if the angle between the dipole moment of the dipole and field is 0 rad or rad, then the torque will be zero.

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