Magnetic monopoles

A magnetic monopole is a single, isolated, north magnetic pole or a single, isolated, south magnetic pole. There is presently no evidence that magnetic monopoles exist. The question of their existence is one of the great unsolved problems in physics. See also: Magnetic monopoles; Physics

Magnetic dipoles

A magnetic dipole is a north magnetic pole connected inseparably to a south magnetic pole. A magnetic dipole moment can either appear as an intrinsic property of a particle, such as an electron, or can arise from a simple loop of electric current, such as in an atom or in a coiled wire. A magnetic dipole moment acts like a small bar magnet. In addition to its intrinsic dipole moment, an atomic electron also has an orbital dipole moment that arises from its circulating motion in the atom. The total dipole moment of the electron is the sum of its intrinsic dipole moment and its orbital dipole moment. See also: Atom; Electron

Magnetic quadrupoles and other multipoles

As a consequence of there being no magnetic monopoles, higher-order magnetic moments must be collections of magnetic dipoles. This means that magnetic tripoles do not exist. A magnetic quadrupole consists of two antiparallel magnetic dipoles. (Note that two parallel magnetic dipoles act dominantly as a single dipole.) A magnetic sextupole consists of three magnetic dipoles, and so forth.

Magnets

A magnet is a macroscopic object that creates a magnetic field and therefore has a magnetic moment. Although most magnets are dipole magnets, higher-order magnets do exist. A magnet contains a collection of electric currents, such as the free currents in an electromagnet or the bound currents in a permanent magnet. Magnets also contain intrinsic dipole moments that can be treated mathematically as bound currents. The four types of magnets are permanent magnets, induced magnets, electromagnets, and induced electromagnets. See also: Magnet

Effect of electric currents

Electric currents always produce magnetic fields. In electromagnets and induced electromagnets, the currents move freely through a conductor. In permanent magnets and induced magnets, the currents are bound in atoms and molecules and consist of circulating electrons. In the 1820s, scientists such as French physicists Jean-Baptiste Biot, Félix Savart, and Andre-Marie Ampère determined quantitatively how electric currents produce magnetic fields and exert magnetic forces. The differential equation summarizing how a current produces a magnetic field is known as Ampère’s law. When cast into a simplified integral form, Ampère’s law is known as the Biot-Savart law. See also: Ampère's law; Biot-Savart law

Effect of intrinsic moments

Intrinsic moments, such as that of an electron, always produce magnetic fields. Along with bound currents, intrinsic moments contribute to the magnetic field of permanent magnets and induced magnets. Because of its dependence on quantum spin, an intrinsic moment can be treated mathematically as a small loop of current. See also: Spin (quantum mechanics)

Effect of changing electric fields

A changing electric field produces a magnetic field. This principle is accounted for by adding an extra mathematical term to Ampère’s law, expanding it into the Ampère-Maxwell law. In practice, the magnetic field that is produced by a changing electric field is often insignificant. The most significant role of this effect is in enabling electromagnetic waves to exist and to be self-propagating. See also: Electromagnetic wave; Electromagnetic wave transmission

Magnetic force on a moving charged particle

The magnetic force law describes how a magnetic field B exerts a force F on a moving charged particle. This law is part of the Lorentz force law, which describes both electric and magnetic forces. The magnetic force law states:

Here q is the particle’s charge, ν is the particle’s velocity, and θ is the angle between the particle’s direction of motion and the direction of the magnetic field. This expression implies that a magnetic field exerts a force on a charged particle only when the particle is moving. This expression also shows that the force is largest when the magnetic field is perpendicular to the direction of motion of the charged particle, and there is no force if the field is parallel to the direction of motion. See also: Motion

The magnetic force law further states that the directionality of the magnetic force is always sideways relative to the motion of the particle. Therefore, the magnetic force can only change the direction of the particle but cannot accelerate it. As a result, a magnetic field can never do mechanical work directly. For a charged particle moving freely in space, the sideways nature of the magnetic force causes the particle to travel along a helical trajectory around the magnetic field lines. This effect can be used to trap free particles magnetically, such as occurs in Earth’s ionosphere and in nuclear fusion reactors. See also: Ionosphere; Nuclear fusion; Particle trap

Magnetic force between magnets

Because all magnets contain collections of currents, magnets exert forces on each other. In principle, the force between two magnets can be calculated using the magnetic force law. In practice, however, such calculations are complicated. For simple magnets, an easier rule can be used: Opposites attract and likes repel. This means that a north magnetic pole attracts a south magnetic pole. It also means that two north poles repel each other and, similarly, two south poles repel each other. Determining the location of the poles of an induced magnet or electromagnet involves additional rules. The force between magnets is the operating principle behind electric motors and audio speakers. See also: Loudspeaker; Motor