How Do You Calculate the Angle of the Net Magnetic Force in a Complex Field?

[Crimsonangel]

One component of a magnetic field has a magnitude of 0.074 T and points along the +x axis, while the other component has a magnitude of 0.020 T and points along the -y axis. A particle carrying a charge of +7.50 10-5 C is moving along the +z axis at a speed of 3.20 103 m/s.

(a) What is the magnitude of the net magnetic force that acts on the particle?

(b) What is the angle that the net force makes with respect to the +x axis?

I figured out the first question using F=Bqvsin90 for X anf Y and then used pythag. to get the answer which was 0.018397 N.

I am having problems with (b). I don't know how to find the angle because it is not on a plane I think. The net force has XYZ components and I don't know how to find an angle for that. Could you please help? Thanks!

 

[Saketh]

In order to keep everything straight, I would advise that you think of this problem in terms of vectors, and not in terms of scalars.

That is, chug through the determinant cross product method to get the net force as a vector, and then use vector analysis to find the angle.

If you are used to thinking of magnetic field problems in terms of scalars, now is a good time to learn this new method.

 

[Crimsonangel]

I don't understand what you mean by "determinant cross product method". I thought that to figure out the direction of the force you use the right hand rule. I figured out the force using F=BqvSin90 and figured out the direction of each force using the right hand rule. I then added the vectors. The direction of the force is on the YX plane.

But I just figured it out. I switched the Y and X directions. Thanks for your help though, I appreciate it!