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Dipole Motion in a Uniform Field

Consider an electric dipole located in a region with an electric field of magnitude E pointing in the positive y direction. The positive and negative ends of the dipole have charges + q and - q, respectively, and the two charges are a distance D apart. The dipole has moment of inertia I about its center of mass. The dipole is released from angle \theta=\theta_0, and it is allowed to rotate freely.

Part A
What is omega_max, 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.
ANSWER:
  omega_max =  \sqrt{\frac{2qDE\left({\cos}\left(0\right)-{\cos}\left({\theta}_{0}\right)\right)}{I}} 
Thus omega_0 increases with increasing theta_0, as you would expect. An easier way to see this is to use the trigonometric identity

 1 - \cos{\theta} = 2 \sin^2{\frac{\theta}{2}}

to write omega_0 as 2 \sin{\frac{\theta_0}{2}}\sqrt{\frac{qED}{I}}.

Part B
If theta_0 is small, the dipole will exhibit simple harmonic motion after it is released. What is the period T of the dipole's oscillations in this case?
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Express your answer in terms of pi and quantities given in the problem introduction.
ANSWER:
  T =  \frac{2{\pi}}{\sqrt{\frac{qDE}{I}}} 
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