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Dipole Moment

Two particles...

Question

Two particles, carrying charges - q and +q and having equal masses m each are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with slightly tilted and then released. Neglecting gravity find the time period of small oscillations.

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Solution

Consider the rod to be a simple pendulum for simple pendulum
$T = 2 π \sqrt{\frac{l}{g}}$
Now, force experienced by teh charges
F = Eq
Now, accln = f/m = Eq/m
Here, Length = a
So, period
$T = 2 π \sqrt{\frac{m a}{q E}}$

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