Problem with find angle btw vectors (magnetism problem)

crevin

1. The problem statement, all variables and given/known data

The x, y, and z components of a magnetic field are Bx = 0.10 T, By = 0.13 T, and Bz = 0.17 T. A 25 cm wire is oriented along the z axis and carries a current of 4.5 A. What is the magnitude of the magnetic force that acts on this wire?

2. Relevant equations
F=ILB (sin theta)
a^2 + b^2 = c^2


3. The attempt at a solution

Well, I have
F= (4.5A)(0.25 m)(B?????) (sin theta)

Ok, so I know what I and L are--> 4.5 A and 0.25 m. I also know that B is going to be the vector sum of components x and y-->
0.10^2 + 0.13^2 = B^2, which gives me B= 0.16. I did not include z because the current is in the z direction (parallel direction = 0, since sin 0 = 0).

My question is: How do I find theta? Theta is the angle between the current and the magnetic field. I know the magnetic field = 0.16 and the direction of the current is in the z-axis, which is 0.17. I was thinking of doing the tan inverse of 0.16/0.17, but I don't think that answer is right.

Any ideas on how to find theta?

Thanks a lot for any help

Sourabh N

theta is invariably 90 deg.
Theta is the angle between B & l. since u have taken Bx & By their resultant is in x-y plane & l is on z axis.
I hope i am clear.

crevin

Yes! Thank Sourabh N for the help-- I've spent over an hour looking at it and couldn't get it!

I finally got the right answer with your advice.

Thanks A LOT!