Why is Magnetic field given as ampere per metre? What does ampere have to do here?

Question

Isn't it just 1 coulomb of electrons passing any cross section per second? Why is it involved here in magnetism?

Rob Jeffries · Accepted Answer

ToAmpere's law can be written (for static fields)
$$oint vec{H}cdot dvec{l} = I_{rm enc} ,$$
where $vec{H}$ is the "magnetic field", which is integrated around a closed path, and $I_{rm enc}$ is the current enclosed by that path.
From this equation it is clear that the H-field has units of A/m (in SI units).
It seems quite likely that you have become confused between the B-field (magnetic flux density, which is often called the magnetic field and has SI units of Tesla) and the H-field (also often called the magnetic field or magnetic field intensity), which has units of A/m.

Anastassis Kapetanakis · Answer

The Biot-Savart law for a steady current gives the magnetic field as follows:
$$vec B(vec r) = dfrac{μ_0}{4π}intdfrac{(vec I times(vec r - vec r'))}{(vec r - vec r')^3}dl$$
Since $vec I$ is in amperes, $vec r$ and $vec r'$ ar in meters, you get that unit for magnetic field

Why is Magnetic field given as ampere per metre? What does ampere have to do here?

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