Soft magnetic material, Faraday's laws

Why soft magnetic material is used for cores

Cores of transformers and armatures carry alternating flux, so in every cycle the material goes round its $B$–$H$ loop. Soft magnetic materials (silicon steel, soft iron, CRGO) are chosen for the following reasons.

• They have a narrow hysteresis loop, so the hysteresis loss (loop area $\times f\times V$) is small.
• They have high permeability, so a large flux is set up by a small magnetising current.
• They have low coercivity and low retentivity, so they magnetise and demagnetise easily without keeping residual magnetism.
• Silicon raises their resistivity, which lowers eddy current loss when the core is laminated.

Faraday's laws of electromagnetic induction

1. First law: whenever the flux linked with a coil changes, an emf is induced in it. The emf lasts only while the flux is changing.
2. Second law: the magnitude of the induced emf is equal to the rate of change of flux linkages:

$$e = -N\frac{d\phi}{dt}$$

The negative sign is Lenz's law: the induced emf drives a current that opposes the change that produced it.

Ways of inducing emf in a coil

1. Statically induced emf: the coil is at rest and the flux linking it changes with time.
   • Self-induced: the coil's own current changes, $e = -L\,di/dt$.
   • Mutually induced: the flux of a neighbouring coil changes, $e = -M\,di/dt$ (transformer action).
2. Dynamically induced emf: the flux is constant, but the coil moves across the field (or the field moves across the conductor). For a conductor of length $l$ moving with velocity $v$ at right angles to field $B$,

$$e = Blv\ \text{volt}$$

This is the principle of generators. A combination of both is also possible, for example a moving coil in a time-varying field.