# Homework Help: Ion beam in E and B field problem

1. Nov 9, 2009

### HPRF

1. The problem statement, all variables and given/known data

A beam of ions enters a region in which the electric field E and magnetic flux density B are normal to each other and both normal to the velocity of the ions. Show that if the velocity of the ions is related to the fields by

v=ExB/B2

then the ions pass through the region undeflected.

2. Relevant equations

Thinking of using

F=qvxB

but not sure.

3. The attempt at a solution

Substituting v from info into Lornetz force equation but it doesn't seem to answer the question.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 9, 2009

### lanedance

so for the ions to pass through unaffected, the force due to the elctric field & the motion through the magnetic must be equal & opposite (ie exactly cancel)

3. Nov 9, 2009

### HPRF

So would it be more accurate to use

qE=qvxB

and then substitute in the v equation?

4. Nov 9, 2009

### lanedance

sounds like a reasonable idea to me, give it a try

couple of pointers though, just be careful with your signs as the forces neecd to cancel out

now you could expand a vector triple product or make use of the orthoganalilty of the vectors in teh question & look at the magnitudes...

5. Nov 12, 2009

### gabbagabbahey

If I were you, I would use the general form of the Lorentz force law $\textbf{F}=q(\textbf{E}+\textbf{v}\times\textbf{B})$, and plug in the velocity you are given...after using some vector triple product identities, you should find that the force on each ion $\textbf{F}$ is zero.