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Magnetic flux density

The magnetic flux density is defined as the density of the field lines. As a so-called B field, it is an indirect measure of the strength of a magnetic field. The designation B-field is wanted: it is not the actual magnetic field, even if the two terms are sometimes used interchangeably in the literature.

Calculate magnetic flux density

While by definition the magnetic flux density is described by the letter B the letter for the magnetic field is H. The following relationship applies with the so-called permeability constants μ0 (for vacuum) and μ (for additional materials):

Formel Magnetische Flussdichte

The permeability constant can vary depending on the type of material:

  • As long as the material is not ferromagnetic, the material-specific permeability constant μ about 1.
  • In the case of ferromagnetic materials, this value can sometimes go up to 100,000.
  • If it is again a superconductor, then μ = 0.
The product of the two permeability constants and the magnetic field H thus by definition gives the magnetic flux density B. It is measured in the Tesla Unit (T).

Background information

Many cannot really use the magnetic flux density formula mentioned above. The descriptive explanation of the physical background should help a little: A so-called magnetic field is formed around a conductor through which electricity flows. This would exert forces on nearby cobalt, nickel, iron or other ferromagnetic materials. The magnetic flux density B in turn indicates how strong this magnetic field actually is. Sometimes it is also called magnetic induction. B describes the density of the magnetic flux through a surface. There are numerous formulas for performing this calculation.

Magnetic flux density vs. magnetic flux – Is there a difference here?

The magnetic flux density that runs through an imaginary surface is the magnetic flux. It is helpful to imagine an image with the magnetic field lines between two poles. The density of the field lines in a cross section is so to say the magnetic flux density.

According to the so-called Maxwell equations - a very well-known physical law in electrodynamics - field lines cannot simply stop. The flux density of a magnet therefore continues to run in its exterior. The magnetic flux itself has the formula symbol Φ and basically denotes the entirety of all magnetic field lines. The magnetic flux therefore results from a certain area A to the product with the magnetic flux density B. The area must be perpendicular to the flux.

Magnetischer Fluss

Moving charges - i.e. currents - cause a magnetic flux. This has no beginning and no end, because currents only create closed field lines. Physically correct, this means that there are no sources and no sinks in the magnetic flux or the magnetic flux density. This fact is the reason why two poles always form a magnet: a south pole and a north pole.

The Maxwell equations from electrodynamics express this fact mathematically. It is important to understand that permanent magnets are also based on this behavior with regard to the magnetic flux density: microscopic circular currents with a current I, are formed there, caused by movements of the electrons in the material. They are responsible for the magnetic flux or the magnetic field. The circular current creates a so-called magnetic moment with the south pole below the conductor loop and the north pole above this conductor loop. If the direction of the current were reversed, the poles would be reversed.

From a physical point of view, the magnetic flux is therefore defined by the inductive effect that it exerts on a conductor loop. If a conductor loop with a known area is brought into a magnetic field, this indicates a surge there. The magnetic flux is equal to the time integral over this surge:

Magnetischer Fluss

The magnetic flux is measured with this conductor loop and the voltage induced in it. However, this is no longer a common method: a so-called Hall probe is much more precise. If the magnetic flux density runs through a curved surface, the magnetic flux is to be defined as an integral over the surface normal of the vectorial flux density:

Magnetische Flussdichte

Field lines that enter through a closed surface - for example, the surface of a sphere - must also exit from there. This is the nature of closed field lines: Mathematically, this is manifested in the fact that the magnetic flux through closed surfaces is always zero. There are therefore no sources or sinks in the magnetic flux density.

Maxwell-Gleichung Divergenzfreiheit

The equivalent of this is the statement of one of the four Maxwell equations about the so-called freedom from divergence of the magnetic flux density.