How to Determine the Magnetic Field B Using Forces F1, F2, and F3 on a Charge?

[waiyat620]

Homework Statement

Let F1,F2 and F3 be the forces experiences by a test charge q at a point in a region of electric and magnetic fields E and B, respectively, for velocities v1,v2 and v3, respectively, of the charge.
If F1,F2 and F3 are such that A= F1xF2 + F2xF3 + F3xF1 =/= 0, that is, their tips do not lie on a straight line when drawn from a commom point.
-> Show that B=(1/q)|(F2-F1)/[(v2-v1)xA]|A

*(The character that Bolded means vector, eg. F1)

Homework Equations

I think it is related to the Lorentz Force Equation.

The Attempt at a Solution

My teacher told us to find the relationship between B and A, which we can assume B=kA and to find k. I don't really have any idea how to work on it as i don't know how to get the direction of each force.
Please Help me..I am really despair as i have worked on it for a really long time ..

 

[BvU]

Hello Waiyat and welcome to PF.

Great post. If you use boldface to designate a vector that's good. An alternative is to use ${\#}{\#}$ \ vec F ${\#}{\#}$ to get $\vec F$.

I think it is related to the Lorentz Force Equation

I agree. So write it down! Not only for me, but for yourself as well.

Under 1. I notice you have v1 etc as scalars first, but as vectors later on. And the B is definitely a B

"teacher told us" is not the same as showing your attempt: you have to start somewhere and get stuck somewhere. Being desperate is not really helpful. Panicking isn't either. Don't worry, help is on the way. Make a first step so potential helpers can see where you are.

Free advice: make a drawing. Doesn't have to be a prize winner, just a simple diagram. If the problem seems too complicated, draw only a few things you do recognize.