# Calculating magnetic force on circular coil carrying current

1. Jan 26, 2015

### cseil

1. The problem statement, all variables and given/known data
A circular coil with center on the z axis and orthogonal to the xy axis carries a current. The coil is in a magnetic field B with axial simmetry compared to the x axis. B forms an angle θ with the z axis. Calculate the magnetic force acting on the coil.

2. Relevant equations

$$\vec{F_B} = i \vec{dl} x \vec{B}$$

3. The attempt at a solution

I tried considering $$dl = r d\phi$$
So $F = irB_zd\phi$
where Bz is $Bcos\theta$

By is null because it has opposite verse on opposite points of the coil. So I can consider just Bz

$$F = irBcos\theta d\phi = irBcos\theta \int_0^{2\pi} d\phi = 2\pi irBcos\theta$$

The result, according to the book, is $2\pi irBsin\theta$
Why?

2. Jan 26, 2015

### Vagn

How does your book define $\theta$? Is it the angle the magnetic field makes with the horizontal(i.e. $B_y$)?

3. Jan 26, 2015

### cseil

It is the angle between B and Bz!

4. Jan 27, 2015

### rude man

What does this mean?

5. Jan 27, 2015

### cseil

I can't understand what does it mean, actually.

6. Jan 27, 2015

### rude man

So ask! The problem is not you, it's the instructor who can't write understandably!