INDUCTION                                       topics

The word means "to bring about". In this sense we are "bringing about" a current from some other form of energy.

The process of inducing a current was first found by Michael Faraday ( 1831 ) who reasoned that since Oersted had shown electricity creates magnetism that magnetism should create electricity. ( This reversability is an example of a symmetry - very important in modern particle physics.)

After much trying, he showed that the key to generating electricity is RELATIVE CHANGE - motion and / or field variation.

• The simplest picture of induction is by considering the hypothetical +q, this time in a conductor, and by externally moving the conductor with a velocity of  v  in a magnetic field  B as in the animation.
• Once again, a force  F = qvBsinθ will exist on q and the RHrule ( fingers start in qv direction to finish in B direction. Thumb gives F. )will apply on the charge to get the direction of F.
• The animation shows that the charge will be "pushed" along the conductor by F so one end will become POSITIVE all the time the motion continues.
• Obviously, the other end will become NEGATIVE. A potential diference between the ends has been created ( and an electric field has been created within the conductor!

Connect the ends to a radio or something - and we will have a current WHILE THE CONDUCTOR IS BEING MOVED. The energy for the radio comes from the motion.

We calculate the generated voltage across the ends of the conductor - the "ELECTROMOTIVE FORCE, EMF, ε" by calculating the

Work Done   = F x distance  = qvBsinθ  x length of conductor  = qvlBsinθ

Well now this ain't so hard,

EMF ( voltage ) =  Work Done / q  = vlBsinθ

If we connect this to a resistance, start invoking Ohm's Law and away we go. EMF = IR

Now that is interesting; we have a current in our conductor! So we can use F = IlB on this current and good old RHScrew rule.

The Force on our induced current OPPOSES the motion, v, of the conductor !!! Ah, so the external mover must do work against this force - THAT is where the energy link comes in.

EXTENSION

Faraday started with this model but logically concluded that any change would do the trick. He introduced the MAGNETIC FLUX idea.

Φ  =  B.Area swept out by conductor          ( Φ = Greek Phi for flux )

Now,  he reasoned that   EMF  =  vlB  = ylB /Δt      where y = distance the conductor moves in time Δt

BUT , but    yl  =  area swept out  = A   in time Δt

SO                   EMF  =  BA / Δt  = Δ Φ / Δt      This is called Faraday's Law ( sometimes Neumann's Law) of Induction.

Why so important ? Because it allows B to change in time!!!!!!   and induce a current.

This is the key explanation to many induced currents where no moving conductors are around, merely changing fields.

Transformers, eddy currents, Induction coils in cars - all work through this principle.