Statically and dynamically induced emf

By Faraday's law an emf is induced in a conductor whenever the flux linking it changes. If the change is caused by movement of the conductor (or field) it is a dynamically induced emf; if the conductor and field are both still and the flux itself changes with time, it is a statically induced emf.

Dynamically induced (motional) emf

A conductor of length $l$ moving with velocity $v$ at angle $\theta$ to a field of flux density $B$ cuts flux and has an emf

$$e = B\,l\,v\sin\theta \quad \text{V}$$

Direction is given by Fleming's right-hand rule.

Depends on:

• flux density B,
• active length of conductor l,
• speed v,
• angle θ between the motion and the field (maximum at 90°).

Example: the armature conductors of a dc generator or the stator conductors of an alternator; the emf of a dc generator is $E = \frac{\phi Z N P}{60A}$.

Statically induced emf

The conductor is stationary and the flux linking it changes. Two kinds:

(a) Self-induced emf: emf induced in a coil by the change of its own current.

$$e = -L\frac{di}{dt}, \quad L = \frac{N\phi}{I} = \frac{N^2}{S} = \frac{\mu_0\mu_r N^2 A}{l}$$

Depends on the number of turns, the reluctance (core material, length, area) and the rate of change of current. Example: the emf in a choke or the spark across a switch when an inductive circuit is opened.

(b) Mutually induced emf: emf induced in one coil by the change of current in a nearby coil.

$$e_2 = -M\frac{di_1}{dt}, \quad M = k\sqrt{L_1L_2}$$

Depends on the turns of both coils, the reluctance of the common path, the coupling coefficient $k$, and $di_1/dt$. Example: the transformer, where an alternating primary current induces an emf in the secondary: $E = 4.44 f N \phi_m$.

Comparison