# Electron Moving in a Uniform Magnetic Field

## Homework Statement

An electron that has a velocity with x component 2.3 x 106 m/s and y component 2.9 x 106 m/s moves through a uniform magnetic field with x component 0.040 T and y component -0.12 T. (a) Find the magnitude of the magnetic force on the electron. (b) Repeat your calculation for a proton having the same velocity.

F = q vXB

## The Attempt at a Solution

Since both magnetic field and velocit were given in component form I figured they could be combined into one (meaning one for velocity and one for magnetic field). After doing

a = sqrt[ (ax)^2 + (ay)^2] for both V and B I got V =3.7 x10 ^6 m/s, angle = 5.158 degrees; B = 1.2649 x 10^-1, angle = -71.565.

Then I added the two angles (I figured their sum is the total difference b/w the B and V vectors?) and plugged in:

F = q v X B
F= (1.6 x 10^-19)(3.7 x 10^6)(1.2649 x 10^-1)sin (-66.407)
F = -6.862 x 10^-14 N

For part b) it should be the same # as the charge of the proton and electron is the same (only sign is different and we use absolute values in that equation).

I hope that my approach is ok, though, assuming my approach is ok I think I might have messed up the combining of the two angles. Any help/guidance would be greatly appreciated. Thank you in advance.

P.S. I thought I should mention that no diagram is provided. Thanks again.

dx
Homework Helper
Gold Member
You got the angle wrong. Also, this is all much easier to do using the components. Both v and B are in the xy plane, so their cross product will have only a z-component. The z component of q(v x B) is just q(vxBy - vyBx).

You got the angle wrong. Also, this is all much easier to do using the components. Both v and B are in the xy plane, so their cross product will have only a z-component. The z component of q(v x B) is just q(vxBy - vyBx).

Hmm by using that, I get an answer of -6.27 x 10^-14, which is incorrect....Just out of curiosity, what would be the correct angle, had I not realized that components were easier? Thanks again, especially for that godly-quick response.

dx
Homework Helper
Gold Member
They asked for the magnitude, so you should remove the minus sign.

dx
Homework Helper
Gold Member
Assuming you calculated the angle of each of the vectors correctly, the angle between them would be 71.565 + 5.158 = 76.723. Just draw a picture and it should be obvious why.

Assuming you calculated the angle of each of the vectors correctly, the angle between them would be 71.565 + 5.158 = 76.723. Just draw a picture and it should be obvious why.

Duh! I can't believe I didn't see that! Also, the answer yielded with your method is correct. Thank you very much!

dx
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Gold Member
No problem.

what about the component qE of the lorentz force?

dx
Homework Helper
Gold Member
E is zero here.