Physics · Chapter 18
Study notes aligned to the official NEB syllabus.
Electromagnetic induction is the production of an electromotive force (EMF), and hence a current, in a conductor whenever the magnetic flux linked with it changes. Discovered by Michael Faraday and Joseph Henry, it is the principle behind generators, transformers, and most of the electrical technology that powers the modern world. This chapter covers Faraday's laws, Lenz's law, motional EMF, the AC generator, eddy currents, self- and mutual inductance, the energy stored in an inductor, and the transformer.
Magnetic flux linked with a coil of area $A$ in a field $B$, where $\theta$ is the angle between $B$ and the normal to the coil, is:
$$\Phi = BA\cos\theta$$
Its SI unit is the weber (Wb). The flux changes if $B$ changes, if $A$ changes, or if the coil rotates so that $\theta$ changes.
Faraday's first law: Whenever the magnetic flux linked with a circuit changes, an EMF is induced in the circuit; the induced EMF lasts only as long as the flux is changing.
Faraday's second law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit.
For a coil of $N$ turns:
$$\boxed{\varepsilon = -N\frac{d\Phi}{dt}}$$
(For a single turn, $\varepsilon = -\dfrac{d\Phi}{dt}$.) The negative sign expresses Lenz's law.
Statement: The direction of the induced current is always such as to oppose the change in magnetic flux that produces it.
Lenz's law and conservation of energy: the negative sign in Faraday's law is a direct consequence of the conservation of energy. If the induced current aided the flux change instead of opposing it, the growing current would produce a growing force and EMF without any external work, creating energy from nothing. By opposing the change, the induced current ensures that the electrical energy generated comes from the mechanical work done against the opposing force.
When a conductor of length $L$ moves with velocity $v$ perpendicular to a magnetic field $B$, the free charges in it experience a magnetic (Lorentz) force $qvB$, which pushes them to the ends and sets up a potential difference. In equilibrium the EMF equals the work done per unit charge:
$$\boxed{\varepsilon = BLv}$$
If the moving conductor is part of a closed circuit, this motional EMF drives an induced current. This is the elementary form of the generator.
Electromagnetic induction is the production of an electromotive force (EMF), and hence a current, in a conductor whenever the magnetic flux linked with it changes. Discovered by Michael Faraday and Joseph Henry, it is the principle behind generators, transformers, and most of the electrical technology that powers the modern world. This chapter covers Faraday's laws, Lenz's law, motional EMF, the AC generator, eddy currents, self- and mutual inductance, the energy stored in an inductor, and the transformer.
Magnetic flux linked with a coil of area in a field , where is the angle between and the normal to the coil, is:
Its SI unit is the weber (Wb). The flux changes if changes, if changes, or if the coil rotates so that changes.
Faraday's first law: Whenever the magnetic flux linked with a circuit changes, an EMF is induced in the circuit; the induced EMF lasts only as long as the flux is changing.
Faraday's second law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit.
For a coil of turns:
(For a single turn, .) The negative sign expresses Lenz's law.
Statement: The direction of the induced current is always such as to oppose the change in magnetic flux that produces it.
Lenz's law and conservation of energy: the negative sign in Faraday's law is a direct consequence of the conservation of energy. If the induced current aided the flux change instead of opposing it, the growing current would produce a growing force and EMF without any external work, creating energy from nothing. By opposing the change, the induced current ensures that the electrical energy generated comes from the mechanical work done against the opposing force.
When a conductor of length moves with velocity perpendicular to a magnetic field , the free charges in it experience a magnetic (Lorentz) force , which pushes them to the ends and sets up a potential difference. In equilibrium the EMF equals the work done per unit charge:
If the moving conductor is part of a closed circuit, this motional EMF drives an induced current. This is the elementary form of the generator.