Magnetic fields
A magnetic field describes the region around a magnet, electric current, or moving charge in which magnetic effects can be observed.
Magnetic field lines provide a useful way to visualise the direction and relative strength of a magnetic field.
Force on a moving charge
A charged particle moving through a magnetic field can experience a force. The force depends on the charge, velocity, magnetic field strength, and angle between them.
F = qvB sin θ
q is charge, v is particle speed, B is magnetic field strength, and θ is the angle between velocity and field.
The force is perpendicular to both the particle's velocity and the magnetic field when the charge moves perpendicular to the field.
Force on a current-carrying wire
A wire carrying current through a magnetic field can also experience a magnetic force. This principle is central to the operation of electric motors.
F = BIL sin θ
B is magnetic field strength, I is current, L is the length of wire in the field, and θ is the relevant angle.
Electromagnets
Electric current produces a magnetic field. A coil carrying current can therefore behave like a magnet, and placing a suitable magnetic material inside the coil can strengthen the effect.
Electromagnetic induction
Changing the magnetic environment of a conductor can induce an electromotive force. This phenomenon is known as electromagnetic induction.
It provides the foundation for electrical generators, transformers, and many other technologies.
ε = −N ΔΦ / Δt
ε is induced emf, N is the number of turns, and Φ is magnetic flux. The negative sign represents Lenz's law.
Magnetic flux
Magnetic flux measures the amount of magnetic field passing through a given surface.
Φ = BA cos θ
B is magnetic field strength, A is the surface area, and θ is the angle between the field and the normal to the surface.
Electric motors
An electric motor converts electrical energy into mechanical motion. A current-carrying coil placed in a magnetic field experiences forces that can produce rotation.
Generators
A generator works on the reverse basic principle of a motor. Mechanical motion is used to change magnetic flux and induce an electrical emf.
In this way, generators convert mechanical energy into electrical energy.
Lenz's law
The direction of an induced current is such that its magnetic effect opposes the change in magnetic flux that produced it.
This is represented by the negative sign in Faraday's law and reflects the conservation of energy.
Quick example
A 0.5 m wire carries a current of 4 A perpendicular to a magnetic field of 0.2 T. What magnetic force acts on the wire?
Using:
F = BIL
F = 0.2 × 4 × 0.5