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## 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 simmetry 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

2. Homework Equations

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

## The Attempt at a Solution

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I tried considering $$ dl = r d\phi $$

So [itex]F = irB_zd\phi [/itex]

where Bz is [itex]Bcos\theta[/itex]

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 [itex]2\pi irBsin\theta[/itex]

Why?