Magnetic permeability and the definition of the amp, Electrical Engineering

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The ampere has been defined (by the International Committee of Weights and Measures in 1946) as the current flowing in two long parallel wires 1 metre apart that produces a force of 2 x 10-7 Newtonsper metre length between the wires.

1884_magnetic permeability.png

So with the same current flowing in both wires spaced 1 metre apart, it is easy to increase the current until a force of 2 x 10-7 Newtons is measured between them. We then know that the current flowing is exactly 1 amp (by definition). This definition also gives the value of k = 2 x 10-7  Newtons.metre/amp

If we express one of the currents in terms of the magnetic field that it produces, then we obtain an equation for the force per metre lengthexperienced by a current carrying conductor in a magnetic field. This is by far the most useful form of the equation in practice:

897_magnetic permeability1.png

Since   k = 2 x 10-7  then we write the new constant as  µwhere

µ0 =  4π x 10-7 Henrys/metre  

(note the Henry is a unit of measure of inductance

µ0 is known as the magnetic permeability of free space


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