Time Period of a Proton in a Magnetic Field

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January 25th 2011, 01:59 PM
alexgeek

Time Period of a Proton in a Magnetic Field
Spent half an hour looking at this problem, but I can't see anyway to get any of the multiple choice answers:
Quote:
Originally Posted by AQA Specimen Paper

Protons, each of mass mand charge e, follow a circular path when travelling perpendicular to a magnetic field of uniform flux density B. What is the time period for on complete orbit?

A $\frac{2 \pi e B}{m}$
B $\frac{m}{2 \pi e B}$
C $\frac{eB}{2 \pi m}$
D $\frac{2 \pi m}{eB}$
All I know is that it should have something to do with:

Thanks

Edit: Oh and the answer is D
January 25th 2011, 05:16 PM
Aryth

You're missing an equation.

Remember that the tangential velocity of an object in circular motion is: $v = \omega r$ so that:

$F = QvB = m\frac{v^2}{r}$

$QB = m\frac{v}{r} = m\omega$

$\omega = \frac{QB}{m}$

We know the formula for period, which is:

$T = \frac{2\pi}{\omega}$

$T = \frac{2\pi m}{QB}$

Since we know the charge, we can fill that in to get:

$T = \frac{2\pi m}{eB}$

I'm not sure why D doesn't match up to this, but I'm almost 95% sure this is right.
January 25th 2011, 11:47 PM
alexgeek

Thanks very much for the reply, will look again when I got some caffeine.
You were right also, I just had a typo in my LaTeX (\pim instead of \pi m).