Learn first: Magnetic field and Ampère's force
Electromagnetic induction, discovered by Faraday in 1831, is the production of electric current by a changing magnetic field. Power-station generators, transformers, induction hobs, metal detectors and wireless chargers all rely on it. The key idea of the topic is simple: the EMF depends not on the flux itself but on how fast it changes.
The "amount" of magnetic field lines passing through a loop is the magnetic flux:
Φ = BS·cos α
Flux can be changed in three ways: by changing B, S or α (rotating the loop).
B = 0.4 T; the normal to a ring of area 50 cm² makes 60° with B. Flux?
When the magnetic flux through a closed loop changes, an induced current appears in it.
ε = −ΔΦ/Δt, for a coil of N turns ε = −N·ΔΦ/Δt
In a 100-turn coil the flux falls by 0.02 Wb in 0.1 s. The coil’s resistance is 10 Ω. Find the EMF, current and charge.
The induced current flows in such a direction that its magnetic field opposes the change in flux that produced it.
Lenz’s law follows from conservation of energy: the energy of the induced current comes from the work of the external force moving the magnet.
Method for finding the direction:
Free electrons in a conductor moving through a field feel the Lorentz force, so a potential difference appears between its ends:
ε = Bvl·sin α
α is the angle between the velocity and B⃗. The current’s direction is given by the right-hand rule (Fleming’s): field into the palm, thumb along the velocity — the fingers show the induced current.
A 0.5 m rod slides on rails at 4 m/s perpendicular to a 0.2 T field. The circuit resistance is 2 Ω. EMF, current and braking force?
When the current in a coil changes, its own flux changes and an EMF appears in it — self-induction. The flux is proportional to the current: Φ = LI.
ε = −L·ΔI/Δt
W = LI²/2
A current of 4 A in a coil with L = 0.5 H falls to zero in 0.02 s. Self-induced EMF and energy released?
Generator. In a coil rotating with angular velocity ω in a magnetic field the flux varies as Φ = BS·cos ωt, so a sinusoidal EMF is induced:
ε = N·B·S·ω·sin ωt, ε_max = NBSω
In power stations a turbine (driven by steam, water or wind) turns the generator’s rotor, converting mechanical energy into electrical energy. In Uzbekistan and many other countries the mains frequency is 50 Hz.
A transformer is two coils on a common steel core. Alternating current in the primary coil makes an alternating flux in the core, which induces an EMF in the secondary coil. Each turn gets the same EMF:
U₁/U₂ = N₁/N₂ = k (turns ratio)
k > 1 gives a step-down transformer, k < 1 a step-up one. A transformer works only with alternating current: direct current gives a constant flux and induces no EMF in the secondary. For long-distance transmission the voltage is raised, so the current falls and the heating loss in the wires (I²R) drops sharply.
Eddy (Foucault) currents arise in solid pieces of metal in a changing field. They heat the pan on an induction hob and are used in melting furnaces, but in a transformer core they are harmful, so the core is made of thin insulated sheets.
A 100-turn coil of area 0.01 m² rotates at 50 Hz in a 0.5 T field. What is the peak EMF?
A transformer has 1100 turns on the primary and 60 on the secondary; the mains voltage is 220 V. Secondary voltage?