# Circular loop with uniform magnetic field

1. Mar 23, 2015

### Shinwasha

1. The problem statement, all variables and given/known data
A current carrying wire is bent into a circular loop with radius R and lies in the XY plane. A uniform magnetic field in the +z direction exists through out the plane of the loop. What is the magnetic force exerted on the loop?

2. Relevant equations
Fb = I lb sin (theta)

3. The attempt at a solution
Since there is no values given and it's all conceptual this is what I got. I'm thinking it's going to be zero because Quadrant 1 and 3 will cancel each other out and quadrant 2 and 4 will cancel out. I'm not sure is correct.

2. Mar 23, 2015

### Simon Bridge

Can you find an equation in terms of variables for the situation?
Do you know of other situations were you have a loop of some shape in a uniform magnetic field to guide you?

3. Mar 24, 2015

### rude man

I would not believe that.
You want to use cylindrical coordinates for this problem. You also need to assume a direction of current which should have been given in the problem.
What is differential force dF on a segment of the loop ds carrying current i? What is the direction of ds in polar coordinates? Of dF? Of F? And finally magnitude |F|?

4. Mar 24, 2015

### Shinwasha

I already turned the homework in, but thanks everyone for the help. I went with the cancelling out because it's what my sense to me. Today the Prof went over the idea.

5. Mar 24, 2015

### rude man

And he didn't say there is a net force either pulling the loop apart or squeezing it together?

6. Mar 25, 2015

### Simon Bridge

Um. Equal forces in all directions usually counts as "zero net force" on the object itself.

If you draw a free body diagram for each element of the loop, you'll see the net force on each part is also zero (since the loop has a constant radius, the reaction forces in each direction along the loop must exactly cancel the magnetic force on the element.) Sure, there is a magnetic force trying to change the value of R. However, OP is probably still at the rigid body modelling stage - so still no net force on the loop.