Electric Charge in a Magnetic Field

Soaring Crane

1) For a particle of mass m and a charge of q moving in a circular path in a magnetic field B, show that its kinetic energy is proportional to r^2, the square of the radius of the curvature of the path.

I started off with the definition of KE: (mv)^2/2 and the fact that a = v^2/r, where F = m(v^2/r).

Then, I thought;

mv^2 = 2*KE and mv^2 = F*r so r = (2KE)/F so r^2 = (4KE^2)/ F^2, but this is probably wrong. What should I do if so?

Thanks.

whozum

What do you know about the strength of magnetic fields in relation to distance R?

Soaring Crane

If B is constant, then r is constant??

whozum

Well typically one would say that backwards, since B is a function of r. What is B as a function of R?

What does B have to be equal to to put the particle in uniform circular motion? Think about the force involved in circular motion, and the force of a magnetic field.

endeavour

Remember:
F=mv²/r
and F=Bqv

also v=(2pi.r)/t