Electronics Engineering · CHAPTER 00 · FOCUSED LESSON
A moving magnetic field induces current: the principle behind generators.
A magnet sitting inside a coil is not enough. Michael Faraday's galvanometer responded only while magnetic flux through the circuit was changing.
Faraday wrapped wire around a paper cylinder to make a coil and connected its ends to a galvanometer. The meter was sensitive to current direction: deflection to one side indicated one polarity, while deflection to the other side indicated the reverse.
He then moved a magnet back and forth inside the cylinder, deliberately changing the magnetic field passing through the coil's area.
As the magnet entered the coil, the needle deflected. When the magnet stopped—even while remaining inside the coil—the needle returned to zero. Pulling the magnet out produced a deflection in the opposite direction. Faster motion produced a larger rate of flux change and a stronger induced voltage.
The correct cause is not motion in isolation but changing magnetic flux linkage. The same effect can be produced by moving the coil, changing current in a nearby coil or changing the geometry of the magnetic circuit.
Faraday's law relates induced electromotive force to the rate of change of magnetic flux. Lenz's law gives the direction: the induced response opposes the change that produced it. This is energy conservation expressed through circuit polarity.
Generators rotate conductors through magnetic fields; transformers vary current in one winding to induce voltage in another. Both are direct descendants of this experiment.
Read the equation together with the physical meaning and SI unit of each parameter.
For a uniform magnetic field over a flat coil area, this becomes Φ_B = B·A·cos(θ).
| Symbol | Physical meaning | SI unit |
|---|---|---|
| Φ_B | Magnetic flux through one turn | weber (Wb) |
| B | Magnetic flux density | tesla (T) |
| dA | Infinitesimal oriented surface area | square metre (m²) |
| S | Surface bounded by the wire turn | m² |
| θ | Angle between B and the surface normal | radian (rad) or degree (°) |
This form assumes every turn links the same magnetic flux.
| Symbol | Physical meaning | SI unit |
|---|---|---|
| λ | Total magnetic flux linkage | weber-turn (Wb·turn) |
| N | Number of turns in the coil | dimensionless (turns) |
| Φ_B | Magnetic flux through one turn | weber (Wb) |
The second equality assumes constant N and equal flux in every turn. The minus sign is Lenz's law: the induced voltage opposes the change that produces it.
| Symbol | Physical meaning | SI unit |
|---|---|---|
| ℰ | Induced electromotive force (induced voltage) | volt (V) |
| λ | Magnetic flux linkage | Wb·turn |
| t | Time | second (s) |
| N | Number of turns | dimensionless (turns) |
| Φ_B | Magnetic flux through one turn | weber (Wb) |
THE IDEA TO REMEMBERA steady magnetic condition produces no continuous induced voltage. The essential variable is the rate at which flux changes.
INPUT
Changing magnetic fluxDETECTOR
GalvanometerDIRECTION
Opposes the changeCOURSE SOURCE · “ELECTRONICS AND TECHNOLOGY” · ALI CHOURBA