Magnetic energy

Magnetic energy is a common form of energy in physics. It is understood to be the energy contained in a magnetic field. Work must be done to generate a magnetic field. This work is then contained in the magnetic field as energy. It can be thought of as the work required to align all the elementary magnets in the material in parallel, i.e. the work required to twist the atomic spins. The parallel aligned elementary magnets in turn have a certain potential energy, namely the magnetic energy.

The amount of magnetic energy stored in a magnet after parallel alignment of the elementary magnets depends on the material. The value of this energy is proportional to the area under the so-called hysteresis curve.

The energy product as a measure of magnetic energy

The magnetic energy can be calculated using the energy product and determines the grade of a magnet. It increases quadratically with the magnetic field. This means that if a magnetic field is twice as large as a second magnetic field but has the same extent, then it contains four times the magnetic energy.

The greater the magnetic energy of a magnetic field, the greater the magnetic forces. They are proportional to the magnetic energy. This means that a magnetic field with twice the energy has twice the magnetic force.

The principle of energy minimisation

The force acting in a certain direction is calculated specifically as a change in magnetic energy in this direction. This can be thought of as a principle of energetic minimisation. If the energetic minimum is reached, there is no direction along which the energy can be further minimised and all forces disappear. If the energy of a magnetic field is minimised when two objects approach each other, a force acts in the direction that contributes to the minimisation, i.e. an attractive force between the two objects. This is exactly the case when a piece of iron is brought closer to a magnet or a magnetic north pole is brought closer to a magnetic south pole.

If, on the other hand, the magnetic field energy is increased, as is the case when like poles approach each other (i.e. north pole to north pole or south pole to south pole), a repulsive force acts.

Between a magnet and a piece of iron or between the opposite poles of two magnets, magnetic energy is present in the air space that is greater than the magnetic energy in the material. If the iron has a magnetic permeability μ, the proportion of energy that passes through the iron is reduced by this factor compared to the energy in the air space.

If the magnet and iron touch, the air space and therefore the field energy in the air space disappears. In physics, forces always act in the direction of an energetic minimum. This can be expressed in general terms using the expression \( \vec{F}=-\vec{\nabla}U\) for every force \( \vec{F}\) in an energy potential U.

Here \( \vec{\nabla}\) denotes the 'derivative vector' in all spatial directions (mathematically also called 'gradient') and can be written as

\( \vec{\nabla}=\left(\begin{array}{c} \frac{\partial}{\partial{x}} & & \frac{\partial}{\partial{y}} & & \frac{\partial}{\partial{z}} \end{array}\right) \)
where \(\frac{\partial}{\partial{x}}\) denotes the 'change' along the x-axis, i.e. the partial differentiation with respect to x.

If the change in energy in one direction is particularly strong in the potential U, a particularly strong force acts in this direction.

Magnetic energy applications

A magnet can also do work. For example, it can attract a piece of iron.

The magnetic energy is then reduced by the amount of work performed. However, the magnetic field does not disappear forever. Thus, the magnet will not be destroyed if you let the magnet attract the iron piece several times and then remove it again, because work must be applied from the outside when the piece of iron is removed. The magnetic energy of the air space then increases again and returns the previously lost amount of magnetic energy to the entire magnetic field of the permanent magnet.

If a magnet in a coil is always rotated in a circle, the circular rotation performs work via the magnetic field, which can be used to generate electricity. The change in the magnetic field leads to the induction of a voltage. This is how a conventional generator works.

Utilisation of Earth's magnetic energy

Many ideas are centred around the utilisation of Earth’s magnetic energy or even cosmic magnetic fields. However, it is not possible to do this along the Earth's surface because the magnetic field here is largely constant. Accordingly, based on the general law \( \vec{F}=-\vec{\nabla}U\), no force acts because the change in the energy potential U, namely \( \vec{\nabla}U\) along the terrestrial surface is zero.

According to Maxwell's equations, there is also no single north or south pole that could be accelerated to the Earth's North or South Pole. In terms of physics, all these ideas about utilising free energy or magnetic energy are preposterous.

Earth's magnetic energy can only be utilised by bringing a ferromagnetic object, which is located far away from Earth's poles, closer to one of the poles. This would reduce the magnetic energy of the Earth's field and could be utilised, for example, by inducing a current.

However, the effect is negligible, as the Earth's magnetic field is very weak. Much more energy is simply gained by falling in the Earth's gravitational field. But the amount of energy is at most as great as the work that has to be done beforehand to remove the object from the Earth.