Magnetic lines of force of a bar magnet shown by iron filings on paper
Main article: Magnetic field
The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.
Maxwell's equations (which simplify to the Biot-Savart law in the case of steady currents) describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electrically charged particles are in motion---for example, from movement of electrons in an electric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" magnetic dipoles arising from quantum-mechanical spin.
The same situations that create magnetic fields (charge moving in a current or in an atom, and intrinsic magnetic dipoles) are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.
When a charged particle moves through a magnetic field B, it feels a force F given by the cross product:
where
- q is the electric charge of the particle,
- v is the velocity vector of the particle, and
- B is the magnetic field.
Because this is a cross product, the force is perpendicular to both the motion of the particle and the magnetic field. It follows that the magnetic force does no work on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is
where θ is the angle between v and B.
One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration (with the middle finger crossing under the index finger), the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also right hand rule.
Magnetic dipoles
Main article: Magnetic dipole
A very common source of magnetic field shown in nature is a dipole, with a "South pole" and a "North pole," terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the north pole of a magnet is attracted to the south pole of another magnet. The Earth's North Magnetic Pole (currently in the Arctic Ocean, north of Canada) is physically a south pole, as it attracts the north pole of a compass.
A magnetic field contains energy, and physical systems move toward configurations with lower energy. When diamagnetic material is placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby lowering the net field strength. When ferromagnetic material is placed within a magnetic field, the magnetic dipoles align to the applied field, thus expanding the domain walls of the magnetic domains. For instance, two identical bar magnets placed side-to-side normally line up North to South (because the magnetic field lines are aligned), resulting in a much smaller net magnetic field (external to the magnet), and resist any attempts to reorient them to point in the same direction. The energy required to reorient them in that configuration is then stored in the resulting magnetic field, which is double the strength of the field of each individual magnet. (This is, of course, why a magnet used as a compass interacts with the Earth's magnetic field to indicate North and South).
An alternative, equivalent formulation, which is often easier to apply but perhaps offers less insight, is that a magnetic dipole in a magnetic field experiences a torque and a force that can be expressed in terms of the field and the strength of the dipole (i.e., its magnetic dipole moment). For these equations, see magnetic dipole.
Magnetic monopoles
Main article: Magnetic monopole
Since a bar magnet gets its ferromagnetism from electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. Even though a magnet is said to have a north pole and a south pole, these two poles cannot be separated from each other. A monopole — if such a thing exists — would be a new and fundamentally different kind of magnetic object. It would act as an isolated north pole, not attached to a south pole, or vice versa. Monopoles would carry "magnetic charge" analogous to electric charge. Despite systematic searches since 1931, as of 2006[update], they have never been observed, and could very well not exist.[11]
Nevertheless, some theoretical physics models predict the existence of these magnetic monopoles. Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge---that is, why the observed elementary particles carry charges that are multiples of the charge of the electron.
Certain grand unified theories predict the existence of monopoles which, unlike elementary particles, are solitons (localized energy packets). The initial results of using these models to estimate the number of monopoles created in the big bang contradicted cosmological observations — the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of inflation (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.[12]
Quantum-mechanical origin of magnetism
In principle all kinds of magnetism originate (similar to Superconductivity) from specific quantum-mechanical phenomena which are not easily explained (see e.g. Mathematical formulation of quantum mechanics, in particular the chapters on spin and on the Pauli principle). A successful model was developed already in 1927, by Walter Heitler and Fritz London, who derived quantum-mechanically, how hydrogen molecules are formed from hydrogen atoms, i.e. from the atomic hydrogen orbitals uA and uB centered at the nuclei A and B, see below. That this leads to magnetism, is not at all obvious, but will be explained in the following.
According the Heitler-London theory, so-called two-body molecular σ-orbitals are formed, namely the resulting orbital is:
Here the last product means that a first electron, r1, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus. This "exchange" phenomenon is an expression for the quantum-mechanical property that particles with identical properties cannot be distinguished. It is specific not only for the formation of chemical bonds, but as we will see, also for magnetism, i.e. in this connection the term exchange interaction arises, a term which is essential for the origin of magnetism, and which is stronger, roughly by factors 100 and even by 1000, than the energies arising from the electrodynamic dipole-dipole interaction.
As for the spin function χ(s1,s2), which is responsible for the magnetism, we have the already mentioned Pauli's principle, namely that a symmetric orbital (i.e. with the + sign as above) must be multiplied with an antisymmetric spin function (i.e. with a - sign), and vice versa. Thus:
,
I.e., not only uA and uB must be substituted by α and β, respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally ri by the discrete values si (= ±½); thereby we have α( + 1 / 2) = β( − 1 / 2) = 1 and α( − 1 / 2) = β( + 1 / 2) = 0. The "singlet state", i.e. the - sign, means: the spins are antiparallel, i.e. for the solid we have antiferromagnetism, and for two-atomic molecules one has diamagnetism. The tendency to form a (homoeopolar) chemical bond (this means: the formation of a symmetric molecular orbital , i.e. with the + sign) results through the Pauli principle automatically in an antisymmetric spin state (i.e. with the - sign). In contrast, the Coulomb repulsion of the electrons, i.e. the tendency that they try to avoid each other by this repulsion, would lead to an antisymmetric orbital function (i.e. with the - sign) of these two particles, and complementary to a symmetric spin function (i.e. with the + sign, one of the so-called "triplet functions"). Thus, now the spins would be parallel (ferromagnetism in a solid, paramagnetism in two-atomic gases).
The last-mentioned tendency dominates in the metals Fe, Co and Ni, and in some rare earths, which are ferromagnetic, whereas most of the other metals, where the first-mentioned tendency dominates, are nonmagnetic (as e.g. Na, Al, and Mg) or antiferromagnetic (as e.g. Mn). Also the diatomic gases are almost exclusively diamagnetic, and not paramagnetic (the oxygen molecule, because of the involvement of π-orbitals , makes an exception, which is important for the life-sciences).
The Heitler-London considerations can be generalized to the Heisenberg model of magnetism (Heisenberg 1928).
The explanation of the phenomena is thus essentially based on all subtleties of quantum mechanics, whereas the electrodynamics covers mainly the phenomenology.
Units of electromagnetism
[edit] SI units related to magnetism
SI electromagnetism units v • d • e |
| Symbol[13] | Name of Quantity | Derived Units | Unit | Base Units |
| I | Electric current | ampere (SI base unit) | A | A (= W/V = C/s) |
| Q | Electric charge | coulomb | C | A·s |
| U, ΔV, Δφ; E | Potential difference; Electromotive force | volt | V | J/C = kg·m2·s−3·A−1 |
| R; Z; X | Electric resistance; Impedance; Reactance | ohm | Ω | V/A = kg·m2·s−3·A−2 |
| ρ | Resistivity | ohm metre | Ω·m | kg·m3·s−3·A−2 |
| P | Electric power | watt | W | V·A = kg·m2·s−3 |
| C | Capacitance | farad | F | C/V = kg−1·m−2·A2·s4 |
| E | Electric field strength | volt per metre | V/m | N/C = kg·m·A−1·s−3 |
| D | Electric displacement field | Coulomb per square metre | C/m2 | A·s·m−2 |
| ε | Permittivity | farad per metre | F/m | kg−1·m−3·A2·s4 |
| χe | Electric susceptibility | Dimensionless | - | - |
| G; Y; B | Conductance; Admittance; Susceptance | siemens | S | Ω−1 = kg−1·m−2·s3·A2 |
| κ, γ, σ | Conductivity | siemens per metre | S/m | kg−1·m−3·s3·A2 |
| B | Magnetic flux density, Magnetic induction | tesla | T | Wb/m2 = kg·s−2·A−1 = N·A−1·m−1 |
| Φ | Magnetic flux | weber | Wb | V·s = kg·m2·s−2·A−1 |
| H | Magnetic field strength | ampere per metre | A/m | A·m−1 |
| L, M | Inductance | henry | H | Wb/A = V·s/A = kg·m2·s−2·A−2 |
| μ | Permeability | henry per metre | H/m | kg·m·s−2·A−2 |
| χ | Magnetic susceptibility | Dimensionless | - | - |
Other units
- gauss — The gauss, abbreviated as G, is the CGS unit of magnetic field (B).
- oersted — The oersted is the CGS unit of magnetizing field (H).
- Maxwell — is the CGS unit for the magnetic flux.
- gamma — is a unit of magnetic flux density that was commonly used before the tesla became popular (1 gamma = 1 nT)
- μ0 — common symbol for the permeability of free space (4π×10−7 N/(ampere-turn)²).
Living things
Some organisms can detect magnetic fields, a phenomenon known as magnetoception. Magnetobiology studies magnetic fields as a medical treatment; fields naturally produced by an organism are known as biomagnetism.
Electricity · Magnetism
