Ampère-Maxwell Law

This proof is about Ampère-Maxwell Law. For other uses, see Ampère's Law.

Theorem

Let $\mathbf B$ be a magnetic field due to a steady current $I$ flowing through a wire $s$.

Then:

$\ds \oint \mathbf B \cdot \rd \mathbf l = \mu_0 I$

where:

the line integral is taken around a closed path

$\d \mathbf l$ is an infinitesimal vector associated with $s$

$\mu_0$ denotes the vacuum permeability.

That is, the line integral of $\mathbf B$ through the area enclosed by the closed path is equal to $\mu_0 I$.

Proof

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