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Flux Density due to Current Flowing in a Long Straight Wire

The flux density at point p is directed out of the plane of the diagram.
There are various ways to remember the relation between the sense of the current and the sense of the field; one is the corkscrew rule.

The magnitude of the flux density depends on a couple of obvious things:
1. The strength of the current, I
2. The perpendicular distance of p from the wire.

The flux density also depends on the medium surrounding the wire.
If r is small compared with the length of the wire then it is found that the flux density does not depend on the length of the wire.
Experiments show that

so we can write

and, as this is a situation in which there is cylindrical symmetry, the constant is written in terms of 2π

The constant μ depends on the medium surrounding the wire and is called the permeability of the medium.
The units of permeability can be found by rearranging the equation to have m by itself. If you do this you will find TmA-1.
However, remembering that 1T = 1NA-1m-1, we see that the units of m can be written as NA-2.
However (again) these units can also be shown to be equivalent to Henry's per metre Hm-1.
We will find the Henry, a unit of inductance, elsewhere...

If the medium is a vacuum, then the permeability is written μo and its value is 4π×10-7 Hm-1.
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