A rather tricky magnetic field problem.

[orionj]

Homework Statement

A proton moves through a region of space where there is a magnetic field $$\vec{B}$$= (0.61$$\hat{i}$$ + 0.36$$\hat{j}$$) T and an electric field
$$\vec{E}$$= (2.8$$\hat{i}$$ - 4.3$$\hat{j}$$) *10$$^{3}$$ V/m. At a given instant, the proton's velocity is $$\vec{v}$$= (6.3$$\hat{i}$$ + 2.9$$\hat{j}$$ - 4.8$$\hat{k}$$) *10$$^{3}$$ m/s.

Determine the components of the total force on the proton.
F$$_{x}$$= ?, F$$_{y}$$= ?, F$$_{z}$$=?

Homework Equations

I assume what needs to be used is the "Lorentz Equation" which is:
$$\vec{F}$$= q($$\vec{E}$$ + $$\vec{V}$$ * $$\vec{B}$$)
and use the q of a proton which is 1.6*10$$^{-19}$$.

The Attempt at a Solution

I attempted to use a cross product of $$\vec{V}$$ and $$\vec{B}$$ and it seemed to be on the right track but I ended up getting stuck on what to do with $$\vec{E}$$ and honestly I ended up getting stuck on the whole problem and not sure at this point where to start and end.

 

[G01]

Your on the right track.

HINT: Try starting by working out the cross product and getting it in terms of components. Then, group all the x component terms together, all the y component terms together, etc. (This includes the E field terms as well.) Do you see how you can get your answer from here on out?

 

[blochwave]

How'd you get stuck on E? V cross B times the scalar q gives you a vector, and q*E is a vector. Do you remember how to add two vectors?

Then you'll have the force vector, with its x, y, and z components

 

[orionj]

I would say I am a bit rusty when it comes to vectors, I did attempt to do the basic vector addition and the answer I imputed the online homework application disliked lol.

 

[orionj]

I got the answers

1.715*10$$^{-16}$$$$\hat{i}$$
-2.195*10$$^{-16}$$$$\hat{j}$$
-7.98*10$$^{-17}$$$$\hat{k}$$

and the homework program told me to check my signs, and told me I was incorrect. What did I do wrong?

 

[orionj]

I keep trying to do the cross product, then adding the vectors together and the third vector never seems to work out right.

 

[Kurret]

I haven't been doing vectors much, but isn't it just possible to take each composant at a time? So for example Fi=Ei*Q + Q*Vk*Bj. Then no vector addition is required.

 

[orionj]

Out of curiousity, what then would be the setup for Fj and Fk?

 

[G01]

What do you get when you work out v X B?

 

[Kurret]

Out of curiousity, what then would be the setup for Fj and Fk?

If my theory is correct, it should be like:
Fj=EjQ-BjVkQ
Fk=EkQ+QVjBi-BjViQ

it seems like the the +/- depends on how you define the positive directions for y/x/z in k/i/j, so I am not sure on these.