Magnetic fields and induction
Moving charges create magnetic fields, and changing magnetic fields create voltages. These two discoveries underlie motors, generators, transformers, and wireless charging.
Currents create magnetic fields
In 1820 Hans Christian Orsted discovered that an electric current deflects a compass needle: currents create magnetic fields. The field around a straight wire forms circles, with direction given by the right-hand rule (thumb along current, fingers curl with the field). A coil, or solenoid, concentrates the field inside it, and an iron core strengthens it greatly, forming an electromagnet.
Magnetic field and flux
Magnetic flux density B is measured in teslas (T). Earth's field is about 25 to 65 microteslas; a fridge magnet is around 5 mT; MRI scanners use 1.5 to 3 T or more. Magnetic flux through a surface is \(\Phi = BA\cos\theta\), in webers. Ampere's law relates the magnetic field around a closed path to the current passing through it.
Forces on moving charges and currents
A magnetic field exerts a force on a moving charge, \(\mathbf{F} = q\mathbf{v} \times \mathbf{B}\), perpendicular to both velocity and field; for a wire of length L carrying current I across a field B, \(F = BIL\). This force spins electric motors, deflects electron beams in old cathode-ray tubes, and steers particles in accelerators.
Faraday's law of induction
In 1831 Michael Faraday discovered that a changing magnetic flux through a circuit induces an electromotive force: \(\varepsilon = -N\frac{d\Phi}{dt}\) for a coil of N turns. The flux can change because the field changes, the coil moves, or the coil's area or orientation changes. Induction is how generators produce electricity and how transformers and wireless chargers transfer energy.
Lenz's law
The minus sign in Faraday's law expresses Lenz's law (1834): the induced current flows in the direction that opposes the change in flux causing it. Dropping a magnet through a copper tube induces currents that slow its fall; electromagnetic brakes on trains and roller coasters use this effect, and it explains the back EMF in inductors and motors.
Magnetic materials
Ferromagnetic materials such as iron, nickel, cobalt, and their alloys strongly concentrate magnetic fields, with relative permeabilities in the thousands. Soft magnetic materials, such as silicon steel and ferrites, magnetise and demagnetise easily, ideal for transformer and inductor cores. Hard magnetic materials, such as neodymium-iron-boron, retain strong magnetism, forming the permanent magnets in motors, headphones, and hard drives.
Eddy currents and losses
Changing flux also induces circulating eddy currents in conductive cores, wasting energy as heat. Transformer and motor cores are therefore built from thin, insulated laminations or from ferrites with high resistivity. Magnetic hysteresis, energy lost each time a material's magnetisation cycles, adds further core loss. Induction cooktops exploit eddy currents deliberately to heat pans directly.
Worked example
A 200-turn coil of area 0.01 m\(^2\) sits in a field that rises uniformly from 0 to 0.5 T in 0.1 s, perpendicular to the coil. The flux change per turn is \(0.5 \times 0.01 = 0.005\) Wb, so \(\varepsilon = 200 \times \frac{0.005}{0.1} = 10\) V. If the field instead changed in 0.01 s, the induced EMF would be 100 V: faster change, larger voltage.
Key takeaways
Orsted (1820) found that currents create magnetic fields, circling wires by the right-hand rule and concentrated by coils and iron cores. Flux density B is in teslas (Earth about 25 to 65 microteslas; MRI 1.5 to 3 T); flux Phi = BA cos(theta) in webers; Ampere's law links field and current. Magnetic forces act on moving charges and currents, F = BIL, driving motors. Faraday (1831): changing flux induces EMF = -N dPhi/dt; Lenz's law sets its opposing direction. Soft ferromagnetic materials form cores; hard ones form permanent magnets such as NdFeB. Laminations reduce eddy-current losses; induction cooking uses eddy currents deliberately.
Flashcard
Currents create magnetic fields
Check your understanding
A coil's induced voltage doubles when the magnetic field changes twice as fast. Which law explains this?