Dipole Motion in a Uniform Field

Consider an electric dipole located in a region with an electric field of magnitude pointing in the positive y direction. The positive and negative ends of the dipole have charges and , respectively, and the two charges are a distance apart. The dipole has moment of inertia about its center of mass. The dipole is released from angle , and it is allowed to rotate freely.

Part A
What is , the magnitude of the dipole's angular velocity when it is pointing along the y axis?
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Express your answer in terms of quantities given in the problem introduction.
 =
Thus increases with increasing , as you would expect. An easier way to see this is to use the trigonometric identity

to write as .

Part B
If is small, the dipole will exhibit simple harmonic motion after it is released. What is the period of the dipole's oscillations in this case?
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Express your answer in terms of and quantities given in the problem introduction.