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A rather tricky magnetic field problem.

  • Thread starter orionj
  • Start date
7
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1. Homework Statement
A proton moves through a region of space where there is a magnetic field [tex]\vec{B}[/tex]= (0.61[tex]\hat{i}[/tex] + 0.36[tex]\hat{j}[/tex]) T and an electric field
[tex]\vec{E}[/tex]= (2.8[tex]\hat{i}[/tex] - 4.3[tex]\hat{j}[/tex]) *10[tex]^{3}[/tex] V/m. At a given instant, the proton's velocity is [tex]\vec{v}[/tex]= (6.3[tex]\hat{i}[/tex] + 2.9[tex]\hat{j}[/tex] - 4.8[tex]\hat{k}[/tex]) *10[tex]^{3}[/tex] m/s.

Determine the components of the total force on the proton.
F[tex]_{x}[/tex]= ?, F[tex]_{y}[/tex]= ?, F[tex]_{z}[/tex]=?

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


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

Answers and Replies

G01
Homework Helper
Gold Member
2,649
16
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?
 
288
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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
 
7
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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.
 
7
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I got the answers

1.715*10[tex]^{-16}[/tex][tex]\hat{i}[/tex]
-2.195*10[tex]^{-16}[/tex][tex]\hat{j}[/tex]
-7.98*10[tex]^{-17}[/tex][tex]\hat{k}[/tex]

and the homework program told me to check my signs, and told me I was incorrect. What did I do wrong?
 
7
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I keep trying to do the cross product, then adding the vectors together and the third vector never seems to work out right.
 
144
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I havent been doing vectors much, but isnt 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.
 
7
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Out of curiousity, what then would be the setup for Fj and Fk?
 
G01
Homework Helper
Gold Member
2,649
16
What do you get when you work out v X B?
 
144
0
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 im not sure on these.
 

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