A straight wire segment of length L makes an angle of 21.0 degrees with respect to the x axis. The wire carries a current of 4.10 A in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the negative z direction with a magnitude given by B=B0(x/L)^3, where B0=3.80 T and L=4.91 m.
What is the force in the y direction from the magnetic field?
If the wire can rotate freely about the z axis what is the magnitude of the torque?
dF=Idl x B
Torque= r x F
The Attempt at a Solution
I found the magnetic force using the first equation
dF=IdL x B and since B is with respect to x i simplified the cross product to dx
And plugged in the equation for B and integrated from 0 to L*cos(theta)
Now for the torque I thought back and if you have the wire laying across the x axis or at least the xz plane and applied a force in the positive y direction you would be rotating about the z axis so i did r x F with the F from the previous answer and r= L*cos(theta). Is that incorrect?