23.2 MATHEMATICAL PROPERTIES

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Magnetic fields have direction. As a result we must pay special attention to directions, and vector calculations.

23.2.1 Induction

Magnetic fields pass through space.

resistivity of materials decreases with temperature

Amperes Circuit Law

Flux density can be calculated for low H values. As the value climbs the relationship becomes non-linear.

Permeability,

Permeability is approximately linear for smaller electric fields, but with larger magnetic fields the materials saturate and the value of B reaches a maximum value.

Figure 23.1 Saturation for a mild steel (approximately)

Figure 23.2 Magnetization curves (Sen, 1989)

Flux density about a wire

Flux and flux density,

When a material is used out of the saturation region the permeabilities may be written as reluctances,

Electric circuit analogy

Example,

Faraday's law,

Field energy,

Force can be derived from the energy,

The basic property of induction is that it will (in the presence of a magnetic field) convert a changing current flowing in a conductor to a force or convert a force to a current flow from a change in the current or the path.

Figure 23.3 The current and force relationship

We will also experience an induced current caused by a conductor moving in a magnetic field. This is also called emf (Electro-Motive Force)

Figure 23.4 Electromagnetically induced voltage

Hysteresis