Magnetism

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What is magnetism?

Magnetism is an umbrella term for all phenomena that are attributed to magnetic forces. Historically, magnetic forces were first observed in stones from the Greek city of Magnesia. The magnet and magnetism are named after the Greek city of Magnesia. The physical science of magnetic and electrical forces was only explained in the 19th century and mathematically formulated in 1864 by James Clerk Maxwell with the help of Maxwell's equations.

Table of Contents

The history of magnetism

Magnetism is the physical phenomenon of magnetic forces. The Greeks recognised electrical and magnetic forces of attraction and repulsion as early as 500 BC. There is evidence of the observation of electrical forces of attraction between small pieces of paper and rubbed amber. The forces acting here are caused by the electrostatic charge of the rubbed amber. In 500 BC in ancient Greece, Thales of Miletus described the force effects of stones from the city of Magnesia on iron particles. The discovery site near Magnesia gave the phenomenon of magnetism its name. It is even thought that the Chinese recognised the powers of the magnetic stone as early as 800 BC, 300 years before the Greek documented observations. The first primitive compass was developed in China around 1000 AD.

Many research scientists have been studying the phenomenon of magnetism since the Renaissance (around 1500). But there was often confusion between magnetism and electricity. Conversely, some scientists considered the two phenomena to be fundamentally different. In 1785, Coulomb confirmed that, unlike electricity, it is impossible to separate a magnet into its north and south pole. If you break a permanent magnet, you always end up with smaller magnets, each with a north and a south pole.

In 1820, Oersted, who was well aware of the difference between electricity and magnetism, recognised the connection between electrical and magnetic forces when he discovered the deflection of a compass needle by a current-carrying wire.

Maxwell's equations: The basic equations of magnetism

A complete explanation of all electrical and magnetic phenomena in the exact physical and mathematical sense was not given until 1864 by the physicist James Clerk Maxwell. He wrote down the Maxwell equations named after him, which fully describe the electric and magnetic fields and the resulting forces. The basic equations of magnetism are two of the four Maxwell equations, which describe the vector fields of the magnetic flux density.

These two time-dependent Maxwell equations for the relationship between the magnetic flux density \(\vec{B}\) with the current density \(\vec{j}\) and the change in electric field strength \(\dot{\vec{E}}\) are as follows:

\(\nabla\cdot\vec{B} = 0\)
and

\(\nabla{\times{\vec{B}}} =\mu_0\cdot\vec{j}+\frac1{c^2}\dot{\vec{E}}\).

The permeability constant of the vacuum \(\mu_0\), the current density \(\vec{j}\) and the speed of light c occur.

According to Maxwell's equations, there are only closed magnetic field lines. This is described by the equation \(\nabla\cdot\vec{B} = 0\). The equation states that the 'open' part of the field lines, i.e. the so-called divergence of the magnetic field, is equal to zero. Mathematically, this is equivalent to saying that there are no magnetic monopoles, i.e. magnets with only one north or only one south pole.

\(\nabla{\times{\vec{B}}} =\mu_0\cdot\vec{j}+\frac1{c^2}\dot{\vec{E}}\) states that closed magnetic field lines are caused either by currents \(\vec{j}\), i.e. by moving charges, or generally by the change in an electric field \(\dot{\vec{E}}\). The latter is relevant for the description of electromagnetic waves, which propagate in space as mutually generating electric and magnetic oscillations. The last-mentioned equation explains Oersted's observation: The magnetic compass needle is itself a small permanent magnet. The current-carrying wire, however, causes magnetic field lines that interact with the magnetic field of the compass needle and exert a force on the needle.

Charges themselves, in turn, generate electrical forces. This is also described by two Maxwell equations:

\(\nabla\cdot\vec{E} = \frac\rho\epsilon_0\)
and

\(\nabla{\times{\vec{E}}}+\dot{\vec{B}} = 0\).

Here, ρ denotes the charge density as the most important source of the electric field \(\vec{E}\). ε₀ denotes the dielectric constant of the vacuum. Closed field lines (rotations) of the electric field \(\nabla{\times{\vec{E}}}\) are caused by the change in the magnetic flux \(\dot{\vec{B}}\) in the same way as closed magnetic field lines.

A clear separation of electricity and magnetism and, at the same time, the standardised description of electricity and magnetism in physics was achieved for the first time by Maxwell's equations. Here, the forces of electricity and magnetism are explained by fields, namely magnetic fields and electric fields.

The illustration schematically shows the magnetic field of a current I (left) (in Maxwell's equations, j denotes the current density, i.e. current in relation to area). The magnetic field surrounds the conductor in closed vortices. The magnetic field of a conductor loop is created accordingly (centre). Many conductor loops together (in 'stacked' form) result in the magnetic field of a coil. This is identical to the magnetic field of a permanent magnet (right). In a permanent magnet, or in magnetised material in general, the electron spins are aligned in parallel. This is equivalent to many circular currents with associated magnetic moments aligned parallel to each other. The external magnetic field is then created by the superposition of the contributions of all elementary magnetic moments.

Today, we speak of the theory of electromagnetism. The theory of time-varying fields of electricity and magnetism is known as electrodynamics. Electrodynamics therefore deals with magnetism and electricity in their entirety.

The effect of magnetic fields on matter is described by so-called 'material parameters' such as magnetic permeability μ. This can also be calculated using Maxwell's equations. But, effects such as magnetisation and electric polarisation must be incorporated into the equations. Today, increasing accuracy in the determination of material parameters and the treatment of quantum objects in quantum electrodynamics have been added to traditional electrodynamics and are current areas of research.

In 2007, the physicist Grünberg was honoured with the Nobel Prize for his discovery of so-called giant magnetoresistance.

Author:
Dr Franz-Josef Schmitt

Dr Franz-Josef Schmitt is a physicist and academic director of the advanced practicum in physics at Martin Luther University Halle-Wittenberg. He worked at the Technical University from 2011-2019, heading various teaching projects and the chemistry project laboratory. His research focus is time-resolved fluorescence spectroscopy in biologically active macromolecules. He is also the Managing Director of Sensoik Technologies GmbH.

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