Deriving Magnetic Field Magnitude using Ampere's Law

[alanthreonus]

Homework Statement

Ampere's Law states $$\int _C \vec{B} \cdot \vec{dr} = \mu_0 \ I$$ .

By taking C to be a circle with radius r, show that the magnitude B = |B| of the magnetic field at a distance r from the center of the wire is $$B = \frac{\mu_0}{2 \pi} \ \frac{I}{r}$$

The Attempt at a Solution

I really don't know where to start. I don't know what the components of B are, so I don't know how I'm supposed to compute this integral.

 

[espen180]

What do you know about the B-field at a distace r from the wire, magnitude-wise? How can you use this knowledge in computing the integral?