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Lesson 36 · The changing flux
It is the change, never the field
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It is the change, never the field

Here is the law the electrical grid is built on: ε=NΔΦΔt\varepsilon = N\dfrac{\Delta\Phi}{\Delta t}, read aloud epsilon equals N delta-phi over delta-t. ε\varepsilon (epsilon) is the induced EMF in volts — EMF stands for electromotive force, which is a terrible name, because it is a voltage and not a force at all; NN is the number of turns, a bare count, and every turn adds its own voltage in series; ΔΦ\Delta\Phi is the CHANGE in flux through one turn, in webers, where Δ\Delta (delta) means “the change in”; and Δt\Delta t is the time that change took, in seconds.

Read the formula as the sentence it is: a coil generates voltage only while the flux through it is CHANGING. Park a coil in the strongest steady field on Earth and it produces exactly zero. A generator is not a magnet near a coil; it is a magnet that will not hold still.

The tidiest case gets its own formula. Slide a straight conductor across a field and it sweeps out fresh area every second — a changing flux with the algebra already done: ε=BLv\varepsilon = BLv, epsilon equals B L v, with BB the field in teslas, LL the conductor's length in metres, and vv its speed across the field in metres per second. No constant, no turns, three multiplications. That is why an aircraft's wingtips sit at a fraction of a volt above each other as it flies through Earth's field — real, measurable, and completely useless.

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 →
vεBL

ε=BLv\varepsilon = B L v

  • ε\varepsilon= Motional EMF (voltage)
  • BB= Magnetic field (magnetic flux density)
  • LL= Conductor length (length)
  • vv= Speed (speed)
Motional EMF (ε = BLv) solver →
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 →