Is the Period of a Charged Particle in a Magnetic Field Speed-Dependent?

[soul5]

Homework Statement

Prove that the time for one revolution of a charged particle moving perpendicular to a uniform magnetic field is independent of it's speed. Write an expression that gives the period T in terms of the mass and charge of the particle and the magnetic field strength.

Homework Equations

Fc=4*pi*^2mr/T^2

Fm=qvB

The Attempt at a Solution

Fc=Fm

v=4*pi*^2mr/T^2qB

is that right?

 

[alphysicist]

Hi soul5,

You're expressions look like they are true, but they don't answer the question. The question asks for the expression for the period, but that expresion is not supposed to have r and v in it.

If you can find a formula for the period in terms of r and v you can use that to eliminate r and v in your equation.

So let's say you have an object moving at speed v in a circular path of radius r. What is the period (time to go once around the circle)? Once you have that, use it to eliminate r and v. What do you get?