Ampère-Maxwell Law
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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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Also known as
The Ampère-Maxwell Law is also known as Ampère's Circuital Law.
Also see
Source of Name
This entry was named for André-Marie Ampère and James Clerk Maxwell.