Magnetic fields
Force on a current-carrying conductor
A magnetic field is produced by moving charges or permanent magnets. A wire carrying current in a field of flux density feels a force , where is the angle between the wire and the field. The force is greatest when they're perpendicular and zero when parallel. Its direction is given by Fleming's left-hand rule. Magnetic flux density is defined as the force per unit current per unit length on a wire at right angles to the field; T N A⁻¹ m⁻¹.
≈ 35 minForce on a moving charge
A charge moving at speed through a field feels , always perpendicular to its velocity. So it does no work: the speed stays constant and, in a uniform perpendicular field, the charge moves in a circle of radius . Crossed electric and magnetic fields let through only charges with (a velocity selector). In a conductor, the magnetic force pushes carriers to one side, creating the Hall voltage .
≈ 40 minMagnetic fields due to currents
A current produces a magnetic field. Around a straight wire the field lines are concentric circles (right-hand grip rule), weakening with distance. A flat coil's field resembles a short bar magnet; a long solenoid gives a strong, uniform field inside, which a soft iron core greatly increases. Two parallel wires each sit in the other's field, so they exert forces on each other: currents in the same direction attract, opposite directions repel.
≈ 30 minElectromagnetic induction
Magnetic flux through an area is (with perpendicular to ), measured in webers. For a coil of turns, flux linkage is . Faraday's law: the induced e.m.f. equals the rate of change of flux linkage. Lenz's law: the induced e.m.f. acts to oppose the change that causes it. Together: . A conductor of length moving at through a field has .
≈ 40 min