Magnetic field

The magnetic field transmits the forces of a magnet. It is a field of electromagnetic energy. The magnetic field strength, therefore, indicates how strong a magnet is. As the amount of magnetic energy is described by the energy product, into which the magnetic field strength is squared, a magnet with twice the magnetic field strength has four times the force effect compared to a magnet with a singular field strength.

Illustrating magnetic fields with field lines

The magnetic field is often represented graphically by field lines. These field lines become visible when iron powder is scattered on a piece of paper with a magnet placed underneath. In such a case, the iron particles arrange themselves parallel to the field lines and show the magnetic field.

Magnetic field lines are always closed, run by definition from the north pole to the south pole of a magnet and are perpendicular to the surface of the magnet. As a rule, moving charges cause magnetic fields. A current-carrying wire therefore also causes a magnetic field.

The magnetic field is a pure dipole field. This means that there are no magnetic charges that could be understood as a single pole, but only magnets with a north and a south pole. It can be mathematically proven that for this reason, the field lines are always closed. They run from the north pole to the south pole and inside the magnet back to the north pole.

Maxwell's equations to describe magnetic fields

The magnetic field is described by Maxwell's equations. Maxwell's equations indicate how dense the magnetic field lines are for a given current distribution and which direction the magnetic field lines have. Maxwell's equations can thus be used to calculate how strong a magnetic field is for given currents and in which directions the magnetic forces act. While there are no sources of the magnetic field, electric charges are the sources of the electric field. This manifests itself in the fact that field lines "run out of" or "run into" the charges. There are no sources of the magnetic field. However, changing electric fields and currents cause magnetic vortices. The magnetic field is, therefore, a pure vortex field.

If many small magnets overlap, the total measurable magnetic field strength is equal to the sum of all the magnetic fields of the small magnets. This principle is known as the superposition principle. From the superposition principle, it follows that many tiny microscopic ring currents in a material, with each leading to an elementary magnet, together cause a measurable magnetisation, i.e. a noticeable magnetic field, if all elementary magnets are uniformly aligned. If, on the other hand, the elementary magnets are randomly orientated, no external magnetic field can be measured.

Calculating magnetic fields

Contrary to popular belief, the magnetic field in physics is not abbreviated with the letter B and, unlike the B field, which denotes the magnetic flux density, is not measured in the units tesla or gauss. Instead, the magnetic field is abbreviated with the letter H and measured in amperes per metre.

The following relationship applies

\( H = \frac{1}{\mu\mu_0}\cdot {B}\)
Here, μ denotes the magnetic permeability of the material that is filled by the magnetic field. μ₀ is the magnetic permeability constant of the vacuum. For the vacuum and by approximation for air, μ=1. For iron, on the other hand, μ can reach values of up to several thousand.

The magnetic flux density of a current-carrying coil is amplified by the factor μ if the coil contains a material with magnetic permeability μ. The magnetic flux density has no sources and no sinks. Thus, it penetrates from the iron into the air space without changing its size. It causes a correspondingly large magnetic field in the air space. Magnetic fields are therefore amplified by contact with ferromagnetic materials.

Picture a magnetic field in a ferromagnetic material that causes the existing microscopic magnetic moments to align in parallel and thus bring about a magnetic flux density themselves. This magnetic flux density can be much stronger (by a factor of μ stronger) than the magnetic flux density that originally aligned the many elementary magnets.

The quadratic dependence of the magnetic forces on the magnetic field strength can be clearly visualised. During the magnetisation of iron in the field of a hypothetical magnet 'M4' with twice the field strength compared to another magnet 'M1' d, the iron is also magnetised twice as much. In turn, the iron, itself magnetised with twice the strength in the field of M4 (compared to M1), is now attracted twice as strongly to the magnet M4 per unit of magnetisation (compared to M1). So the total magnetic force effect and the total amount of magnetic energy in magnet M4 is four times greater than in M1. The force effect and the energy product increase quadratically with the magnetic flux density or the magnetic field.