Calculating magnetic force on circular coil carrying current

[cseil]

Homework Statement

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 symmetry compared to the x axis. B forms an angle θ with the z axis. Calculate the magnetic force acting on the coil.

2. Homework Equations

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

The Attempt at a Solution

[/B]
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?

 

[Vagn]

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

 

[cseil]

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

It is the angle between B and Bz!

 

[rude man]

The coil is in a magnetic field B with axial symmetry compared to the x axis.

What does this mean?

 

[cseil]

What does this mean?

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

 

[rude man]

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

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