Finding Magnetic Field using Lorentz Force

[derrickb]

Homework Statement

Show that two measurements F₁ and F₂ of magnetic force at a fixed point are sufficient enough to determine B at that point as (see picture) provided v₁ and v₂ are orthogonal.

2. Homework Equations
F = qv x B
B_z = cF_x/(qv_y)
B_y = cF_z/(qv_x)
B_x = cF_y/(qv_z)

The Attempt at a Solution

I have 3 pages of various attempts that I can upload if necessary. I can't seem to figure out what the orthogonality has anything to do with and to be honest, the professor wrote this down on the board and he could have forgotten an exponent or something like that. If someone could even just give me a hint as to what the orthogonal velocities has anything to do with, I may be able to figure it out from there.

 

[lightgrav]

he means that you only need v_x and v_y , if you know all components of their Forces

 

[derrickb]

I'm a little confused by what you're saying. Why don't you need the z-components of the velocities?

 

[derrickb]

Nevermind I just remembered there is no force caused by the velocity in the direction of the field. So you mean you only need v_x and v_y if B is in the z-direction?

 

[lightgrav]

If F_1,z is applied to qv_x , what does that tell you? (yes, B_y)
If F_2,z is applied to qv_y , what does that tell you? (your original post doesn't have this)

 

[derrickb]

That would tell you B_x?

 

[lightgrav]

actually its negative.
Each component of F has 2 contributions from each cross-product. example: F_z = qv_x B_y - qv_y B_x
(OMG! qv x B = - B x qv ! is this cool?)