Magnetostatics

The magnetostatics is a branch of electrodynamics. They treated DC magnetic fields, ie temporally constant magnetic fields.

Basics

In magnetostatics, the spatial distribution of magnetic fields in the vicinity of permanent magnets and stationary currents (the concept of current thread ) is investigated. A steady-state current, for example, direct current in an electrical conductor. They include the individual magnetic properties of materials such as ferromagnetism, diamagnetism, etc. also the geomagnetic field. In addition, the magnetostatics describes the force of such generated fields on magnets and currents. This includes the behavior of a magnetic dipole in a temporally constant magnetic field, for example, the behavior of a ( freely moving ) magnetic needle in the magnetic field.

The basic terms are the electrostatic analogy. The positive and negative electric charge corresponding to north and south poles, quantitatively: positive and negative pole strength. However, magnetic poles, in contrast to electric charges are not isolated, but occur in a body to always be together.

Illustration

Although there are no isolated magnetic charges ( magnetic monopoles ), magnetostatic effects with an analogy to electrostatics can be illustrated. This is used particularly in high school physics: one considers a bar magnet of length l as two opposed magnetic charges at a distance L. The analogue of the electric charge is the magnetic pole strength. It is of the same dimension as the magnetic flux and is thus expressed in the unit Weber.

It is then the magnetic force law (also magnetostatic force law ): Between two magnetic poles of the pole strength and the distance the magnetic force acts

Here, μ0 is the magnetic field constant.

It follows, for example, in a homogeneous field having a known flux density B and the area A for the force:

Field theory

For time-constant fields " decouple " the equations for electric (E) and magnetic (B ) fields: you sit in the Maxwell equations all time derivatives equal to 0, arise equations containing E and B are not the same. Can be described with the following two reduced Maxwell equations The phenomena of magnetostatics:

It leads the vector potential as an auxiliary field with the following definition:

Thus, the equation is automatically fulfilled, since the divergence of a field is the same as rotation 0.

However, is not uniquely determined, since is invariant under a gauge transformation with. That by A and A ' set B fields are identical. This comes from

Since the rotation of the gradient of a scalar field vanishes.

Substituting in the inhomogeneous Maxwell equation ( equation 2)

A, we obtain the Coulomb gauge the particularly simple form:

This is a Poisson equation for each component is represented by

Is dissolved.

If we apply the rotation to A at one obtains the Biot- Savart law for the physically relevant B-field

For a current thread is about:

Magnetostatic fields

Magnetostatic fields exist within the same current-carrying conductor. They are free of sources and there is no magnetic charges,

The cause of magnetostatic fields are moving electric charges or functionally equivalent DC currents with the vortex density: