In magnetostatics, the spatial distribution of magnetic fields in the vicinity of permanent magnets and of stationary currents (concept of the current filament ) is examined. A stationary current is, for example, direct current in an electrical conductor . In addition to the individual magnetic properties of substances such as ferromagnetism , diamagnetism, etc., this also includes the earth's magnetic field . In addition, magnetostatics describes the force effect of such fields on magnets and currents. This includes the behavior of a magnetic dipole in a time-constant magnetic field, for example the behavior of a (freely movable) magnetic needle in the earth's magnetic field.
The basic terms are analogous to electrostatics . The positive and negative electrical charge correspond to the north and south poles, quantitatively: positive and negative pole strength . However, in contrast to electrical charges, magnetic poles cannot be isolated, but always appear together in a body.
Although there are no isolated magnetic charges ( magnetic monopoles ), magnetostatic effects can be illustrated with an analogy to electrostatics. This is particularly used in school physics: one considers a bar magnet of length l as two opposing magnetic charges at a distance l . The analogue of the electric charge is the magnetic pole strength . The pole strength is defined in such a way that the magnetic force law (also: magnetostatic force law ) can be formulated analogously to the Coulomb force :
Here F is the magnetic force that acts between two magnetic poles of the same pole strength and at a distance ; μ 0 is the magnetic field constant . The pole strength is of the same dimension as the magnetic flux and is therefore given in Weber units .
From the definition it follows e.g. B. for a homogeneous field with known flux density B and area A for the force:
For fields that are constant over time, the equations for electric (E) and magnetic (B) fields “decouple”: if all time derivatives in Maxwell's equations are set equal to 0, equations arise that do not contain E and B at the same time . The phenomena of magnetostatics can be described with the following two reduced Maxwell equations:
The vector potential is introduced as an auxiliary field with the following definition:
This automatically fulfills the equation , since the divergence of a rotational field is identical to 0 .
however, is not clearly determined because it is invariant under a gauge transformation with . I.e. the B fields defined by A and A ' are identical. This follows from
since the rotation of the gradient of a scalar field vanishes.
If we put into the inhomogeneous Maxwell equation (above equation 2)
a, the Coulomb calibration results in the particularly simple form:
This represents a Poisson equation for each component , which is given by
If one applies the rotation to A , one obtains the Biot-Savart law for the physically relevant B field
For a stream filament goes to :
Magnetostatic fields exist within conductors carrying direct current. They are source-free and there are no magnetic charges,
The cause of magnetostatic fields are moving electrical charges or equivalent direct currents with the vortex density:
- Wolfgang Demtröder : Experimental Physics. Vol. 2: Electricity and optics . Springer, Berlin 2004, ISBN 3-540-20210-2
- Wolfgang Nolting : Basic Course Theoretical Physics 3: Electrodynamics . Springer, Berlin 2007, ISBN 978-3-540-71251-0
- Adolf J. Schwab: Conceptual World of Field Theory, Springer Verlag, ISBN 3-540-42018-5
- You can also find the definition . In this case the pole strength has the dimension “current strength × length” and the unit A · m.