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Electricity and Magnetism

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Moderate

Change in Kinetic Energy of a Dipole in a Rotation

EANDM-KDFNS5

Figure 1A depicts the initial position of a dipole in a uniform electric field in the $xy$-plane, in which the dipole is aligned at an angle of $\theta_0 = 90^{\circ}$ with respect to the positive $y$-axis. Figure 1B depicts the position of the dipole some time later, in which the dipole is aligned at an angle of $\theta_f = 60^{\circ}$ with respect to the positive $y$-axis.

Figure 1A and 1B

Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

The magnitude of each of the two point charges is $q = 14.6 \text{ mC}$, and the charges are separated by a distance $d = 40.6 \text{ mm}$ from one another. The electric field is:

$$\vec{E} = -1130 \hat{y} \ \rm{\text{N}/\text{C}}$$

What is the change in the kinetic energy of the dipole as it moves from the initial configuration of Figure 1A to the final configuration of Figure 1B?

A

$\Delta K = 0.826 \text{ J}$

B

$\Delta K = 0.335 \text{ J}$

C

$\Delta K = 0.207 \text{ J}$

D

$\Delta K = 0.0897 \text{ J}$