(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Problem 5.4 Suppose that the magnetic field in some region has the form [itex] B=kz \hat{x} [/itex] 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.

2. Relevant equations

[tex] \vec{F} = I \int d\vec{l} \times \vec{B} [/tex]

3. The attempt at a solution

Now i can easily prove that the forces in the two sides that are in line with tehe Y axis cancel out

For the segments parallel to the Z axis however things are a bit different

on the top segment for z>0

[tex]F = i \frac{a}{2} k \frac{a}{2} (\hat{-z}\times\hat{x}) = \frac{ika^2}{4} \hat{y}[/tex]

For the bottom segment z>0

[tex]F = i \frac{a}{2} k \frac{a}{2} (\hat{z}\times\hat{x}) = -\frac{ika^2}{4} \hat{y}[/tex]

For the top segment z<0

[tex] F = i \frac{a}{2} k \frac{-a}{2} (\hat{-z}\times\hat{x}) = -\frac{ika^2}{4} \hat{y}[/tex]

For the bottom segment z<0

[tex] F = i \frac{a}{2} k \frac{-a}{2} (\hat{z}\times\hat{x}) = \frac{ika^2}{4} \hat{y}[/tex]

but dont all these forces jsut cancel to zero??

where have i gone wrong?? I know the answer cant be zero because this is not a uniform field...

Thanks for your help!!

(edit: i have changed the diagram since i had done it wrong, the current should have been in the opposite direction)

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# Homework Help: Simple loop question

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