Finding force produced by a Magnetic Field on a Proton

[MikeBriganti]

Homework Statement

A Proton moves with a velocity of 5x10^6 m/s in the +y direction. What is the force (magnitude and direction) on the proton if a magnetic field of 2.12Ti + 2.12Tj is applied.

Homework Equations

- F = |q|vBsinθ
- Right hand rule to find direction

The Attempt at a Solution

I think that I'm overlooking some math for this problem, and I'm require to use some more trig or something. I would really appreciate it if anyone could help me point out if I did something wrong, and how to go about fixing my mistake.

In the i direction, I had the magnitude of the force equal to (1.6x10^-19)(5x10^6)(2.12)(sin90) which equals 1.696 x 10^-12. I set the magnitude of the force in the j direction equal to 0, because the sin of the angles between the V and the B is equal to 0, in what I think sets that whole force equal to 0.

Then using the right hand rule, I get the final force equal to - 1.696 x 10^-12N k

 

[HallsofIvy]

Why are you taking \theta to be 90 degrees? Shouldn't you use the angle between the velocity vector of the proton and the magnetic field vector, which would appear to be 45 degrees?

 

[MikeBriganti]

Wow, I clearly wasn't thinking straight when I did that problem.. 45degrees makes complete sense. No idea why I thought I attempted to split up the magnetic field components.

Oh well, thank you for your help!

 

[gneill]

Note that since you are given the v and B vector components, you could consider using the vector form of the equation and just do the cross product: $F = q \vec{v} \times \vec{B}$ .

 

[MikeBriganti]

Note that since you are given the v and B vector components, you could consider using the vector form of the equation and just do the cross product: $F = q \vec{v} \times \vec{B}$ .

Unfortunately, I do not know how to do cross products yet.

 

[gneill]

Unfortunately, I do not know how to do cross products yet.

Ah. That's a shame. It avoids having to work out the angles between vectors, which can be annoying if they're 3D. How about determinants? Have you learned how to compute the determinant of a 3x3 matrix?

 

[MikeBriganti]

No I haven't learned to do that either. I'm taking calculus 2 right now, and I'm assuming most of that stuff is taught in Calc 3?

 

[gneill]

No I haven't learned to do that either. I'm taking calculus 2 right now, and I'm assuming most of that stuff is taught in Calc 3?

I think I first came across them in pre-calculus and linear algebra. But if you haven't seen them yet, you'll just have to carry on the way you're going (or take a detour and read up on cross products and determinants).

 

[barryj]

Wait, didn't MikeBriganti get the problem correct the first time?? The component of the magnetic vector in the j direction will have no effect?