Self-Induction

• If moving a coil in a magnetic field induces a current and that current induces a magnetic field, then the induced magnetic field will also have an effect on the coil’s own induced current.
• This self-induction will decrease the efficiency of the generation of a voltage.
• The self-induced emf produced is also known as “back-emf”. The effects of back-emf are more significant at higher currents so it needs to be considered as part of the design parameters.

Alternating current (ac) generators

∙Recall Faraday’s law:

∙From the formula we see that there are three ways to increase the induced emf of a rotating coil:
(1) Increase the number of turns N in coil.
(2) Increase the flux change ΔΦ.
(3) Decrease the time Δt over which the flux changes.

FYI

∙Recall that Φ = BA cos θ. Given the uniform magnetic field and rotating coil, B and A are constant. Thus the flux change ΔΦ will be due only to the change in the angle Δθ.

Alternating current (ac) generators

∙Consider the rectangular loop of wire made to rotate in the fixed magnetic field shown:

 
∙At this instant
Φ = BA cos 0º = BA.
∙A bit later θ has changed:
Φ = BA cos 45º = 0.7BA.
∙When θ = 90º:
Φ = BA cos 90º = 0.
∙As θ continues to increase, the flux Φ becomes negative.
∙A sinusoidal pattern emerges.

 Since \(\varepsilon = -\frac{\Delta \Phi}{\Delta t}\), we see that the induced emf \(\varepsilon\) is the negative slope of the flux.
 Since the slope of the cosine plot is proportional to the sine graph, we see that \(\varepsilon \propto BA \sin \theta\).

This is the basis for Alternating Current (AC) generators and is how we get much of our electricity. You should know that a rotating coil in a magnetic field will produce a sinusoidal emf, but further understanding of AC power generation is not part of the course.