A simple electric dipole in an external magnetic field performs harmonic motion (for small angles between E and L) due to the moments by the forces acting on the respective charges. Assuming there is no system to dissipate energy that is. The mechanic moment is given by p x E and the energy of the system is given by -p.E(adsbygoogle = window.adsbygoogle || []).push({});

We were asked to calculate the period of this harmonic motion. I tried using conservation of energy to find it and I found something but I'm suspecting it's not correct.

What I've found:

At theta Pi/2, both the kinetic energy and the energy of the dipole rotation are zero, which means that their changes are equal.

When looking at theta = 0 this gives:

p*E = I * omega^2 / 2 which gives us omega after one fourth of the period.

Alpha = d omega / dt and I * Alpha = p x E .

So Alpha * (t2-t1) = omega2-omega1 (approximately) and Alpha = p x E /I

Putting these together and using omega1 = 0:

omega2/(T/4) = sqrt(p*E*2/I)/(T/4) = p x E / I which gives:

T= sqrt(p*E*2/I)*4*I)/(p x E)

It's too easy to be correct.. Where did I make an error (if indeed I did and how could I find the real solution?

Thanks !

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# Homework Help: Period of an electric dipole rotating in an external electric field

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