How EMF is generated

Reference notes

This animation steps through five ideas a freshman needs to "feel" before any machine equation makes sense. Hit Next → on the narrator above to walk through the story; the voice-over and the canvas update together.

Faraday's law (Steps 3 & 5)

For an N-turn coil, the induced EMF equals the number of turns times the rate of change of magnetic flux linkage. The magnitude comes from |dΦ/dt|; the negative sign encodes the direction (and that's Lenz's law — see below).

Lenz's law — the direction of the induced EMF (Step 4)

Faraday's law tells you how big the induced EMF is. Lenz's law tells you which way it points:

• If Φ is increasing into the page, the induced current goes counter-clockwise, creating flux out of the page — fighting the increase.
• If Φ is decreasing into the page, the induced current reverses to clockwise, creating flux into the page — trying to maintain what's being lost.

The minus sign in Faraday's equation is Lenz's law. In every machine you'll meet — transformers, motors, generators, induction machines — Lenz's law decides the polarity of every induced quantity. (Examples: armature reaction in alternators, the back-EMF of a motor, the secondary MMF in a transformer.)

Two ways to make dΦ/dt nonzero

• Move the conductor through a steady field. The area swept by the loop changes in time, so Φ changes. Generators do this.
• Hold the conductor still and change the field. The area is fixed, but B is changing, so Φ changes. Transformers do this.

Motional EMF (Step 2)

For a straight conductor of length L moving with velocity v perpendicular to a field B, the induced EMF is the simple product B·L·v. Use the right-hand rule (thumb = velocity, fingers = B, palm pushes positive charges) to get the polarity.

Transformer EMF and the 90° phase shift (Steps 3 & 5)

Here the loop area A and number of turns N are fixed. The whole time-variation lives in B(t). Suppose B varies sinusoidally:

Then differentiating:

This is a 90°-phase-shifted sinusoid. The EMF leads the flux by 90° in time — when the flux is at its peak, dΦ/dt = 0 and the EMF is zero; when the flux is crossing zero, dΦ/dt is largest and the EMF is at its peak.

The 4.44·f·N·Φ_max equation (Step 5)

Taking the RMS value of e(t) above and using ω = 2πf:

This is the most-used formula in transformer and machine analysis — you will derive everything else from it.

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