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Problem 52 Hard Difficulty

Experiments show that a steady current $ I $ in a long wire produces a magnetic field $ \textbf{B} $ that is tangent to any circle that lies in the plane perpendicular to the wire and whose center is the axis of the wire (as in the figure). $ \textit{Ampere's Law} $ relates the electric

Answer

$$
\begin{aligned} \int_{C} \mathbf{B} \cdot d \mathbf{r} &=2 \pi r B=\mu_{0} I \\ B &=\frac{\mu_{0} I}{2 \pi r} \end{aligned}
$$

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