# Magnetic field question

1. Nov 11, 2008

### bakin

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

A very thin wire, which follows a semicircular curve C of radius R, lies in the upper half of the x-y plane with its center at the origin. There is a constant current I flowing counter clockwise, starting upward from the end of the wire on the positive x axis and ending downward at the end on the negative x axis. The wire is in a uniform magnetic field, which has magnitude Bo and direction parallel to the z axis in the positive z direction. Determine a symbolic answer in unit vector notation for the total force on the wire due to the magnetic field. Ignore the forces on the leads that carry the current into the wire at the right end and out of the wire at the left end.

Solution check: The numerical value with I = 2.00A, Bo = 3.00T, and R = 4.00m is 48.0j N.

2. Relevant equations

dFb= i dLxB

3. The attempt at a solution

Because it's curved, I don't think you can use Fb = iLBsin. Instead, the cross product version above has to be used. I read some lecture notes here: http://www.wfu.edu/~matthews/courses/phy114/ppt/Ch29-Magnetic_Fields.ppt [Broken]
And it says that you can just take the length from one endpoint to the other, and use that as your dL. Using that works, because (2)(3)(2x4) = 48, but I don't understand why. Can anybody help clarify? Thanks!!

Last edited by a moderator: May 3, 2017
2. Nov 11, 2008

### Staff: Mentor

The magnitude of the cross product i dL X B = i dL B sinθ. (What's θ?)
Where does it say that? Set up the integral of dF over the length of the semicircle. (It's an easy integral.) Which way does dF point at each position along the arc?

Last edited by a moderator: May 3, 2017
3. Nov 12, 2008

### bakin

Soooo helpful. I was able to figure it out after thinking about your questions a little bit. Thanks for helping me understand!

4. Nov 12, 2008