6.9 Magnetic Quantities and Units

6.9 Magnetic Quantities and Units

Then, the magnitudes in a magnetic circuit (and their corresponding units) are shown now on:

Important Magnetic flux, Ф (Weber, Wb).

Magnetic flux is the set of lines of force passing through a magnetic circuit. These lines of force are always closed on themselves. The unit that we measure magnetic flux in the international system is the Weber (Wb).

Important Magnetic induction, B (Tesla, T).

Magnetic induction, or flux density, is the flux per unit area. This is what happens if the flux is evenly spread across the whole surface:

B=ΦS (6.1)

Important Magnetomotive force (MMF).

It is the work that would be required to carry a hypothetical isolated magnetic pole of unit strength completely around a magnetic circuit. Flux circulates in a magnetic circuit due to the application of magnetic force. A coil having N turns through which current I flows produces a magnetomotive force of:

Fmm=N·I (6.2)

The international system uses the ampere-turn as its unit of measurement (At).

Important Magnetic field strength (H).

Magnetic field strength or magnetizing force is the ratio of the applied magnetomotive force (MMF), in ampere-turns (At), to the length of the magnetic circuit consuming it.

We measure the length on the mean magnetic line, L, as.

H=FmmL (6.3)

The unit of measurement in the International System is (ampere-turn)/meter (At/m). The magnetic permeability of vacuum (μ0) is 4π-10–7 H/m, in the international system.

We use ferromagnetic materials to make electrical machines because it is important to keep the magnetic flux inside them.

Important Permeability (μ). The permeability of a material measures the ability of that material to conduct magnetic flux through it. Conversely, relative permeability (μr) quantifies the capacity to conduct flux with respect to vacuum. The relative magnetic permeability of air has a value of one.

Important Reluctance (ℜ). The reluctance of a magnetic circuit (in Ampere-turn/Wb) is the resistance of the magnetic circuit to the flow of flux through it. This is similar to that of "resistance" in an electrical circuit. The reluctance in a circuit of length L, constant cross section S and material of permeability μ is defined as:

ℜ = L/μ·S (6.4)

This expression shows that the higher the value of the permeability of the material, the lower the value of the reluctance and, the less resistance the circuit presents to the flux. Materials behave differently according to the flux density and magnetic field (Fig. 6.21). It includes B—flux density, H—magnetic field, μf—permeability of ferromagnets (and ferrimagnets), μp—permeability of paramagnets, μ0—permeability of free space (4π × 10⁻⁷ H/m), μd—permeability of diamagnets.

Fig. 6.21 B—flux density, H—magnetic field, μf—permeability of ferromagnets (and ferrimagnets), μp—permeability of paramagnets, μ0—permeability of free space (4π × 10⁻⁷ H/m), μd—permeability of diamagnets. Source From wikicommons under free to use license [20]

This is the reason for manufacturing electrical machines' magnetic circuits using ferromagnetic materials (logically excluding the air gap in rotating machines).