## MATHEMATICAL PROPERTIES

• 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,  • 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