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Reminder sheet

Induction & self-induction

Bastaya

Changing the flux through a coil gives birth to a voltage: that is induction. Lenz adds that the effect always opposes its cause.

Faraday: any change of magnetic flux through a circuit induces an EMF E = −N·ΔΦ/Δt. Lenz: the induced current opposes the cause producing it (minus sign). A conductor cutting field lines at speed v gets E = B·l·v.

Self-induction: a coil opposes changes of its own current, E = −L·ΔI/Δt; L is the inductance, in henries. It stores W = ½ L I². When an inductive circuit is opened, the overvoltage strikes an arc: it is suppressed by a diode or an RC network.

Formulas

Faraday's lawE = −N · ΔΦΔt
QuantitySymbolUnit
Induced EMFEV
Number of turnsN-
FluxΦWb
Timets
Cut fluxE = B · l · v
QuantitySymbolUnit
Magnetic flux densityBT
Lengthlm
Speedvm/s
Self-inductionE = −L · ΔIΔt
QuantitySymbolUnit
InductanceLH
CurrentIA
Energy of a coilW = ½ · L · I²
QuantitySymbolUnit
EnergyWJ
RL time constantτ = LR
QuantitySymbolUnit
Time constantτs

Worked example

The flux through a 200-turn coil drops from 2 mWb to 0 in 10 ms: what induced EMF? A coil L = 0.5 H carrying 2 A: what energy does it store, and what voltage appears if the current is cut in 1 ms?

E = N · ΔΦ / Δt = 200 × 2 × 10⁻³ / 10 × 10⁻³ = 40 V (Lenz's minus sign only gives the direction: the induced current opposes the disappearance of the flux).

W = ½ · L · I² = 0.5 × 0.5 × 4 = 1 J.

E = L · ΔI / Δt = 0.5 × 2 / 10⁻³ = 1 000 V: hence the arc when an inductive circuit is opened, and the freewheeling diode that suppresses it.

Common mistakes

  • Forgetting the number of turns N: every turn sees the flux change, the EMFs add up.
  • Leaving Δt in milliseconds: 10 ms = 0.010 s, otherwise the EMF is a thousand times too small.
  • Reading the minus sign as "negative voltage": it is Lenz's law, the induced current opposes the cause that produces it.

IEC symbols

Coil

Illustration

SNi

Lenz: as the north approaches, the loop creates a north facing the magnet to repel it.

Frequently asked questions

Why does a spark jump when a relay is opened?
The coil opposes the sudden loss of its current: E = L·ΔI/Δt becomes huge when Δt is very short, and the air breaks down between the contacts. A freewheeling diode gives the current a path to die out gently.
What is the difference between induction and self-induction?
Induction: the changing flux comes from outside (a magnet, another coil), as in a transformer or an alternator. Self-induction: the coil reacts to the change of its own current, hence its inductance L.

20 exercises in this topic

This chapter is covered by the paths: General electricity, ISL-oriented exercises

All sheets · All formulas · Glossary of electrical quantities · Standard electrical symbols (IEC 60617)

Practise this topic
Simulated time00:00:00
Q = I·t-
W = P·t-

Workbench

Circuit diagram CEI 60617

How does it work?

The perfboard: each big hole is a circuit node. You push a single leg of a component (resistor, lamp...) into it. The 4 small holes around it are connected to it: that is where chips and leads plug in.

  1. Drag a component onto the board: it snaps onto the grid. R rotates it.
  2. To join neighbouring big holes, click Jumper chip in the palette (or C) then drag on the board: a line of chips is laid at once. Bridged holes become a single node.
  3. For long links and for the power supply (placed next to the board), drag a lead from one big hole to another (or to a terminal).
  4. As soon as a loop is closed, the circuit is solved in real time (Ohm + Kirchhoff) and the diagram follows.
  5. Zoom with the wheel (or + / −, two-finger pinch); drag the background to pan, 0 fits the board. The + buttons around the board add a row or a column.

Del delete · R rotate · C chip brush · Esc cancel · wheel zoom · drag the background to pan

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