What Is the Force on a Square Loop in a Magnetic Field?

[wakko101]

The problem:

Suppose that the magnetic field in some region has the form B = kz (x-hat). Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current I, flowing counterclockwise, when you look down the x axis.

When I try to visualize the direction of the four magnetic fields (one for each side) it seems to me that they would cancel out (one going to the right, one going to the left, one going up and one going down). I have information to the contrary so I'm wondering what it is I'm seeing that is wrong.

Cheers,
W. =)

 

[nicksauce]

For the top & bottom portions of the loop (ie at fixed z), the sign of z changes, but so does the sign from the cross-product, thus the top & bottom parts do not cancel out, but rather add together.