Magnetic flux and magnetic flux density

What do the magnetic flux and magnetic flux density indicate?

The magnetic flux Φ can be understood as the totality of all magnetic field lines. The magnetic flux density B describes the density and direction of the field lines that pass through an imagined surface in space. If the field lines run in a straight line (for example between the poles of a horseshoe magnet), then the magnetic flux Φ through a certain area A, which is perpendicular to the flux, is the product of the magnetic flux density B and the area A: Φ = B•A

Indirectly, the magnetic flux density (B field) is also a measure of the strength of the magnetic field. However, it is not entirely correct to refer to the B field itself as a magnetic field, even if this is occasionally found in the literature. The magnetic field is usually abbreviated with the letter H and the relationship B=μ₀ μ•H with the magnetic permeability constant of the vacuum µ₀ and a material-specific magnetic permeability constant µ applies. However, it is usually around 1, except for ferromagnetic materials, for which µ can assume values of up to 100 000 and for superconductors where µ=0. The product of µ,µ₀ and magnetic field H results in the B field, i.e. the magnetic flux density B.

The magnetic flux density is measured in tesla (T). The magnetic flux correspondingly in Tm². The unit 1 Tm² is also referred to as 1 weber (Wb).

The remanence of a magnetised material is the magnetic flux density that emanates from the material after magnetisation. It is also given in tesla.

Currents as a cause

Magnetic flux is caused by currents, i.e. by the movement of charges. Currents will always create closed field lines. The magnetic flux, therefore, has no beginning and no end. Or, if you want to put it in physics terms, there are no sources and sinks of magnetic flux density and magnetic flux.

This, in turn, is the reason why a magnet must always have two poles: a north pole and a south pole. Mathematically, this is expressed by Maxwell's equations. An electromagnet is a typical current-driven magnet.

In permanent magnets, too, microscopic circular currents I, namely movements of the electrons in the material, are responsible for the magnetic flux and thus also for the magnetic field. These circular currents cause a magnetic flux B, which emerges from the circular current (current loop), runs in an arc to the underside of the current loop and closes again there (cf. illustration). The circular current creates a magnetic moment with the north pole above the conductor loop and the south pole below the conductor loop. If the direction of the current is reversed, the north and south poles are also swapped.

Determining the magnetic flux

Accordingly, the magnetic flux is physically defined by its inductive effect on a conductor loop. If a conductor loop with a known area is placed in a magnetic field, a voltage surge is induced. The time integral over this voltage surge is equal to the magnetic flux Φ:

\(\int{U_{ind}dt}=B\cdot{A}=\Phi\)
Using a conductor loop and the voltage induced in this conductor loop, the magnetic flux can therefore also be measured. However, a more precise Hall probe is usually used for this purpose.

Determining the magnetic flux density

If you consider the magnetic flux density B, which runs through a curved surface, the magnetic flux must be determined as the integral of the vectorial flux density over the surface normal:

\(\int{\vec{B}d\vec{A}}=\Phi\)
Since the field lines are closed, all field lines passing outwards through a closed surface (e.g. a spherical shell) must also pass back into the sphere and vice versa. In mathematical terms, this means that the flux through closed surfaces is always zero and, equivalently, there are no sources or sinks of magnetic flux density:

\(\oint_{A-geschlossen}{\vec{B}d\vec{A}}=0 \Leftrightarrow \vec{\nabla}\cdot{\vec{B}}=0\)
This is equivalent to the so-called freedom from divergence of the magnetic flux density, as stated by one of Maxwell's four equations.

In our FAQ section, you will find a table in Excel or OpenOffice format that you can use to conveniently calculate the flux density of magnets.

Go to table with formulas for flux density calculations