Finding Magnetic Force on a Moving Electron

[bbbbbev]

Hi. Ok, here's the problem:

An electron that has velocity v = (3.6 106 m/s) i + (3.7 106 m/s) j moves through a magnetic field B = (0.03 T) i - (0.15 T) j.

(a) Find the force on the electron.

I know how to find the force from scalar numbers (using the equation F_mag = q x v x Bsin(phi)), but I can't figure out how to do it with vectors. I know that the answer is going to be in the "k" direction, but I don't understand how to get a k from an i and a j, and I can't find how to do it in the book or on any website.

I tried finding the force in the i direction and then the force in the j direction and doing vector addition, but that didn't work because the resultant vector is not in the k direction. I guess the real problem is that I don't know how to add j and i vectors to get a k vector. Could someone please help? Thanks a lot! Beverly

 

[quasar987]

Howdy Beverly. I'm sure you have seen written somewhere the magnetic force in terms of vector as

$$F_{mag} = q(\vec{v} \times \vec{B})$$

This means that the vector force has a magnitude given by vBsinO (like you did) and a direction given by the right hand rule.

Learn about the right hand rule here.

 

[bbbbbev]

Oh, thanks. I think I get it. Can I just find force in the i direction and then find force in the j direction and then multiply them together to get the magnitude in the k direction? I tried doing this:

F_i = q x v_i x B_i
F_i = (1.6E-19C)(3.6e6m/s)(0.03T)
F_i = 1.728E-14 N

F_j = q x v_j x B_j
F_j = (1.6E-19C)(3.7e6m/s)(-0.15T)
F_j = -8.88E-14 N

Then I multiplied F_i x F_j to get F_k, but that answer was incorrect. Am I understanding the right hand rule thing wrong??

Thanks for your help,

Beverly

 

[jdavel]

bbbbbev,

No, you can't do it that way. Go back to the equation you started with:

F =qvBsin(phi) where phi is the angle between the directions of v and B.

Can you figure out what phi is?

 

[quasar987]

I know how to find the force from scalar numbers (using the equation F_mag = q x v x Bsin(phi)), but I can't figure out how to do it with vectors.

The scalar force IS the magnitude of the vector force. The right hand rule only adds to it by telling you the direction of the force based on the directions of the vectors v and B.

 

[bbbbbev]

Thanks! I got it. I figured out phi and just used that equation. Thanks guys.