(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electric dipole (something that has charge +q on one end and charge -q on the other end separated by a distance 2a) is in a uniform horizontal electric field of magnitude E. Initially the electric dipole is aligned horizontally until it is displaced slightly by an angle theta from the horizontal. Show that the electric dipole undergoes simple harmonic motion with frequency given by

[tex]f=\frac{1}{2\pi}\sqrt{\frac{(m_{1}+m_{2})qE}{2m_{1}m_{2}a}}[/tex]

2. Relevant equations

[tex]I\alpha=\tau_{net}[/tex]

[tex]\omega=2\pi f[/tex]

[tex]F=qE[/tex]

[tex]\theta(t)=A\cos(\omega t)[/tex]

3. The attempt at a solution

Here is what I got

[tex]I=(m_{1}+m_{2})a^2[/tex]

[tex](m_{1}+m_{2})a^2\frac{d^2\theta}{dt^2}\approx 2aqE\theta[/tex]

and the frequency I get pops out as

[tex]f=\frac{1}{2\pi}\sqrt{\frac{2qE}{(m_{1}+m_{2})a}}[/tex]

Can't see where I have gone wrong

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# Homework Help: Electric dipole in an electric field

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