What is the Radius of an Electron Trajectory in a Magnetic Field?

[11thHeaven]

Homework Statement

Electrons (mass m, charge –e) are accelerated from rest through a potential difference V and are then deflected by a magnetic field B that is perpendicular to their velocity. Find the radius of the resulting electron trajectory.

Homework Equations

[tex]F=\dfrac{mv^2}{r}[/tex] [tex]F=qvB[/tex]

The Attempt at a Solution

I don't know where to start with this. The electron moves through the potential difference, and presumably gains kinetic energy, but I don't know how to express this in the equations above to get an answer.

Help appreciated.

 

[grzz]

I am assuming that the e is accelerated through a gap across which there is a potential difference V. What is the width of the gap?

 

[11thHeaven]

I am assuming that the e is accelerated through a gap across which there is a potential difference V. What is the width of the gap?

That's all the info I'm given; I've literally copied and pasted the question.

I'm not being asked to give a numerical answer though. It's a multiple choice question, and this is apparently the answer:

[tex]\frac{\sqrt{2mV/e}}{B}[/tex]

 

[grzz]

The p.d. gives an energy of Ve to the electron.

From this one can find the resulting velocity of the electron.

 

[11thHeaven]

The p.d. gives an energy of Ve to the electron.

From this one can find the resulting velocity of the electron.

Aha! Got it. Thanks for the help :)