Along straight wire carries a current $I$. What is the magnitude of the magnetic field at a perpendicular distance $r$ from the wire?

Solution

1. According to Ampere's Law, the line integral of the magnetic field is $\oint B\cdot dl={\mu }_{0}I$.
2. For a circular path of radius $r$, $B(2\pi r)={\mu }_{0}I$.
3. Solving for $B$, we obtain $B={\mu }_{0}I/(2\pi r)$.
4. Hence the answer is (B).