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?