# Wire loop in magnetic field

1. May 10, 2010

### Saraharris38

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

Suppose that the magnetic field in some region has the form
B = k z ˆx.
(where k is a constant). Find the force on a square loop of side a, lying in the yz plane
and centered at the origin, if it carries a current I flowing counterclockwise when looking
down the x axis.

2. Relevant equations

Magnetic force=Integral (I X B) dl

3. The attempt at a solution

The force on the two vertical sides of the loop cancel each other out, and we are left with a top force of I(a/2)B= I((a^2)/2)k. The answer is I(a^2)k, meaning that at the bottom horizontal portion of the loop, the magnetic force is upwards. My question is why would it be upwards, given that the magnetic field is out (in the x direction), and the current, traveling counter-clockwise, is to the right at this part? According to the right-hand rule, shouldn't the magnetic force here be downwards?

Thanks!

2. May 10, 2010

### nickjer

At the bottom of the loop the magnetic field is in the (-x) direction since z<0. So the force experienced in the bottom section would be upwards as well.

3. May 10, 2010

### Saraharris38

Ah! Thank you, that makes sense.