Glossary — Fields

Coulomb constant — the constant $k = \dfrac{1}{4\pi\varepsilon_0} = 8.99 \times 10^{9}\,\text{N}\,\text{m}^{2}\,\text{C}^{-2}$, which appears in Coulomb's law and in the field of a point charge.

Coulomb's law — the electric force between two point charges in a vacuum, $F = \dfrac{kQq}{r^{2}}$. The force is attractive for opposite charges and repulsive for like charges.

Cyclotron — a machine that sends charged particles round a circle many times in a magnetic field so that they gain energy each time they cross an electric field.

Eddy current — a current induced in a piece of metal by a changing magnetic field. Eddy currents can be useful, as in an induction hob, or wasteful, as in a transformer core.

Electric field — the region around a charge in which another charge feels a force. Its field lines point away from a positive charge and towards a negative charge.

Electric field strength — the force per unit positive charge at a point, $E = \dfrac{F}{Q}$. Its unit is the newton per coulomb, or the volt per metre.

Electric potential — the energy per unit positive charge at a point, taking the potential as zero at infinity. For a point charge, $V = \dfrac{kQ}{r}$. Its unit is the volt.

Electromagnetic induction — the creation of an emf in a conductor by a changing magnetic flux.

Equipotential surface — a surface on which the potential is the same at every point. No work is done moving a charge along it, and the field lines are at right angles to it.

Escape speed — the smallest speed a body needs to leave a planet and never return, $v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}}$.

Faraday's law — the induced emf equals the rate of change of the magnetic flux linkage, $\varepsilon = -N\dfrac{\Delta\Phi}{\Delta t}$.

Field line — a line drawn to show the direction of a field. The direction of the line is the direction of the force on a small test body placed at that point, and the lines are closer together where the field is stronger.

Fleming's left-hand rule — the rule for the direction of the force on a current-carrying wire in a magnetic field. The first finger points along the field, the second finger along the current, and the thumb gives the force.

Flux linkage — the magnetic flux through a coil multiplied by the number of turns, $N\Phi = NBA$. Its unit is the weber.

Force field — a region in which a body feels a force without anything touching it, such as a gravitational, electric or magnetic field.

Gravitational constant — the constant $G = 6.67 \times 10^{-11}\,\text{N}\,\text{m}^{2}\,\text{kg}^{-2}$, which appears in Newton's law of gravitation.

Gravitational field strength — the gravitational force per unit mass at a point, $g = \dfrac{F}{m} = \dfrac{GM}{r^{2}}$. Its unit is the newton per kilogram.

Gravitational potential — the energy per unit mass needed to move a small mass from infinity to a point, $V = -\dfrac{GM}{r}$. It is negative, because the potential is zero at infinity.

Induced emf — the emf created by a changing magnetic flux, by Faraday's law. It drives an induced current if the conductor forms a complete circuit.

Lenz's law — the induced current flows in the direction that opposes the change that produced it. The law is a statement of the conservation of energy.

Magnetic field — the region around a magnet, a current or a moving charge in which a magnetic force can be felt. Its field lines are closed loops.

Magnetic flux — the product of the magnetic flux density and the area at right angles to the field, $\Phi = BA$. Its unit is the weber.

Magnetic flux density — the quantity that describes the strength of a magnetic field, symbol $B$, measured in tesla. It is defined by $F = BIL$ for a wire at right angles to the field.

Mass spectrometer — an instrument that accelerates ions, deflects them in a magnetic field, and separates them by mass. The radius of the path is $r = \dfrac{mv}{BQ}$.

Newton's law of gravitation — the gravitational force between two point masses, $F = \dfrac{GMm}{r^{2}}$. The force is always attractive.

Permittivity of free space — the constant $\varepsilon_0 = 8.85 \times 10^{-12}\,\text{F}\,\text{m}^{-1}$, which appears in the Coulomb constant $k = \dfrac{1}{4\pi\varepsilon_0}$.

Radial field — a field whose lines point towards or away from a single point, such as the gravitational field of a sphere or the electric field of a point charge.

Search coil — a small coil of many turns used to measure a changing magnetic field from the emf it induces, $\varepsilon = NA\dfrac{\Delta B}{\Delta t}$.

Tesla — the unit of magnetic flux density, $\text{T}$. One tesla is the flux density that gives a force of one newton on a wire of length one metre carrying a current of one ampere at right angles to the field.

Transformer — two coils wound on the same core, used to change an alternating voltage. The turns ratio sets the voltage ratio, $\dfrac{V_s}{V_p} = \dfrac{N_s}{N_p}$.

Uniform field — a field whose strength and direction are the same at every point, drawn with parallel, equally spaced field lines.

Weber — the unit of magnetic flux, $\text{Wb}$. One weber is one tesla metre squared, $\text{T}\,\text{m}^{2}$.