# Electron velocity when beam is restored by a magnetic field.

1. Jun 18, 2009

### angelabean

A beam of ions is deflected by the electric field between two plates 5cm apart with a p.d. pf 500 volts. It is found that this deflection is restored by a magnetic field of o.2T so that the ions continue in a straight line.

What is their velocity (ions) ?

So far I am thinking:

upward force, F=qE E=v/d, 500V/ 5exp-2m = 1exp4 Vm^-1

Downward force F=mv^2/ r = Bev

F= mv^2/r^2

I have some idea of what I need to do but some clarification would be great.

2. Jun 18, 2009

### lanedance

Hi angelabean & welcome to PF

I think you're pretty much there... if you assume the magentic field is applied along the same length as the electric field, then to restore the path, the magnetic force must exactly balance the electric force. So I would equate them & solve for v.

I would also be careful with your notation as you have used v for both potential difference & velocity. (I would use V for potential difference, as long as its not confused with the units) ;)

3. Jun 24, 2009

### jix

You don't need the circular motion equation (if that's what it is). The forces of the magnetic and electric fields are simply opposite each other, and equating will give you the answer.