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Lesson 55 · Flux and Faraday
Flux, and the rate that makes it pay
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Flux, and the rate that makes it pay

A field on its own induces nothing. What generates voltage is a field CHANGING through a loop — and to talk about that you first need a word for how much field a loop catches. That word is flux: Φ=BAcos⁡θ\Phi = B A \cos\theta, read aloud phi equals B A cosine theta, where Φ\Phi is the Greek capital phi.

Φ\Phi is the magnetic flux in webers (Wb); one weber is a tesla-square metre, and benchwork runs in milliwebers. BB is the field in tesla, AA is the loop's area in square metres, and θ\theta is the tilt angle — and read this one carefully, because it is measured from the loop's normal, the line sticking straight out of its face, NOT from the loop's surface. So a loop facing the field square-on is θ=0\theta = 0, cos⁡θ=1\cos\theta = 1, and it catches every last line. Turn it edge-on at 90∘90^\circ and it catches none. Most problems quietly assume face-on and never mention the angle; when a question does mention it, it is mentioning it for a reason.

Now the law that pays out. Faraday's law: ε=NΔΦΔt\varepsilon = N \dfrac{\Delta\Phi}{\Delta t} — epsilon equals N delta-phi over delta-t, with ε\varepsilon the Greek letter epsilon, the induced EMF in volts. NN is the number of turns in the coil, a plain count. ΔΦ\Delta\Phi — delta-phi — is the CHANGE in flux in webers, not the flux that was there; Δt\Delta t is the time the change took, in seconds. The delta always means “how much this shifted”.

Two nuggets. Δt\Delta t sits underneath, so speed is everything: the same flux change over a tenth of the time gives ten times the volts, which is exactly how an ignition coil turns 12 V into a spark. And this is a two-step problem by nature — flux first, its rate second — so write the flux down on its own line before you go anywhere near a voltage.

θBΦA

Φ=BAcos⁡θ\Phi = B A \cos\theta

  • Φ\Phi= Magnetic flux (magnetic flux)
  • BB= Magnetic field (magnetic flux density)
  • AA= Loop area (area)
  • θ\theta= Tilt angle (angle)
Magnetic Flux (Φ = BA cos θ) solver →
εΔΦΔtN

ε=NΔΦΔt\varepsilon = N \frac{\Delta\Phi}{\Delta t}

  • ε\varepsilon= Induced EMF (voltage)
  • NN= Number of turns
  • ΔΦ\Delta\Phi= Flux change (magnetic flux)
  • Δt\Delta t= Time interval (time)
Faraday's Law of Induction solver →