Finding the magnetic force in square loop wire.

[bfusco]

Homework Statement

Suppose that the magnetic eld in some region has the form B = kzx(hat). (where k is a
constant). 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.

The Attempt at a Solution

Apparently the horizontal sides of the loop are to generate forces that cancel each other out, leaving the forces generated on the vertical parts to add.

Using the Right hand rule, i see no reason why the horizontal parts should cancel and the vertical shouldn't.
Extablishing the +z axis pointing up, and the +y axis pointing right, with the x-axis pointing out of the page.

denoting the bottom (horizontal) part of the loop as 1, the right (vertical) part of the loop as 2, the top (horizontal) part of the loop as 3, and the left (vertical) part of the loop as 4.

In 1) Idl x B = y(hat) x x(hat)=-z(hat)
In 2) Idl x B = z(hat) x x(hat)=y(hat)
In 3) Idl x B = -y(hat) x x(hat)=z(hat)
In 4) Idl x B = -z(hat) x x(hat)=-y(hat)

1 should cancel 3, and 2 should cancel 4

Or is it that B is a function of z, so when the current is going in the +z direction B is in the +x direction, and when the current is going in the -z direction B is in the -x direction? I am not sure

 

[TSny]

Or is it that B is a function of z, so when the current is going in the +z direction B is in the +x direction, and when the current is going in the -z direction B is in the -x direction? I am not sure

I'm not sure exactly what the phrase "looking down the x-axis" means in the statement of the problem, but I think you have the right idea. Since $\vec{B} = kz\hat{x}$, B points in the positive x direction when z is positive and points in the negative x direction when z is negative.