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

A particle of charge q in a vector potential

[tex]\vec{A} = (B/2) (-y\vec{i} + x\vec{j} )[/tex]

show that a classical particle in this potential will move in circles at an angular frequency [tex]\omega_0 = qB/ \mu c[/tex], [tex]\mu[/tex] is the mass of the particle.

2. Relevant equations

3. The attempt at a solution

I write a Hamiltionian as

[tex] H = \frac{1}{2\mu} \left( \vec{p} - \frac{q}{c} \vec{A} \right)^2 [/tex]

and then get

[tex] \mu \dot{x} = p_x + \frac{qB}{2c}y[/tex]

[tex] \mu \dot{y} = p_y - \frac{qB}{2c}x[/tex]

and then I'm lost. I'm not sure if this is right, and if it is: how do I see how this gives circular orbits and what the angular frequency is?

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# Homework Help: Mechanics, charge in vector potential

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