What is Magnetism? – Part 2 (Moving Charges)

In Part 1, we looked at magnetism created by unpaired electrons in the outer orbits of atoms that make up a permanent magnet. When all the domain boundaries of a magnetic material are broken down and the magnetic dipoles of all the constituent atoms are forced into the same alignment by a strong external magnetic field, a permanent magnet is created. When the external field is removed, the internal magnetic field remains.

This type of magnetism is an inherent, quantum-spin effect of unpaired electrons and all observers will see a magnetic field from a permanent magnet regardless of their relative velocities to the magnet.

The second type of magnetism is created by moving charges, positive or negative.

Wherever you have moving charges, you have a corresponding magnetic field. If the charge is stationary, then there is no magnetic field.

Magnetism Produced by Moving Charges is a Relativistic Effect

If you see a static charge, you can measure an electric field, but no magnetic field. An observer who sees your static charge as a moving charge will measure both an electric field and a magnetic field. As this is the same charged particle, the difference is that in one frame of reference it's stationary, in the second it's in motion.

Consequently, the magnetic field produced by moving charges must be a relativistic effect.

In physics, electric and magnetic fields are the two components of the electromagnetic field. The appearance of excitations in the electromagnetic field depends entirely on an observer's frame of reference. If an observer moves at exactly the same velocity as a charged particle, then that observer will only see an  electric field. As soon as the observer slows down or speeds up, the magnetic field manifests itself. The faster the observer moves, the stronger the magnetic-field becomes.

When the relative velocity  of the observer is low compared to the speed of light, then the value of B (the magnetic flux density) measured by the observer, is proportional to velocity. Once the observer starts to approach the speed of light, then Lorenz length contraction results in the value of B increasing dramatically.

For those with a mathematical interest in the effect, the maths can be seen below, where the Lorentz factor affects all calculations.  The closer that the velocity is to that of light, the greater the Lorentz effect.

Magnetism is not separate from electricity. It arises from electricity in motion, which boils down to charged particles in motion.

An Evolving Magnetic Pattern

If you look at the image at the top of the article, the electric field of a stationary particle is shown as a static electric field, radiating out in 3D rather than just the 2D of the drawing.

The pattern shown for a moving charge also looks like a static pattern, but represents the electric and magnetic fields at an instance in time - you can think of it as a frozen image of the two fields. In reality, these fields are moving in the direction of propagation of the particle and are constantly re-arranging themselves as the particle moves from location to location. The geometry of these delayed updates naturally gives rise to the transverse, circulating component that we identify as the magnetic-field loops around moving charges or a current.

In vector language;

The cross product is automatically perpendicular to both the velocity and the electric field, resulting in a circulating magnetic field.

This behaviour is encoded mathematically, so to speak, by Maxwell's equations and the Lorentz transformation, but it also provides an intuitive picture of why the magnetic field wraps around the direction of motion rather than pointing out radially.

So, the magnetic loops that we detect around a current aren't 'painted onto' space, they evolve as every point in space is receiving retarded (time-delayed) information about the moving charge, resulting in reconfiguration of the field until a loop around the current results.

Magnetism Acting on Single Charged Particles

Both permanent magnets and electro-magnets are used to control particle streams in accelerators. The resulting magnetism performs a number of tasks;

1. Bending particle tracks to ensure they stay inside a synchrotron ring like the LHC for example, without crashing into the walls as they are accelerated.

2. Focussing beams, preventing particles from diverging.

3. Increasing magnetic-field strength in line with increasing velocity as particles reach relativistic speeds to enable continued acceleration.

4. Channeling particle streams in a particular direction to extract beams from accelerators and channel to bombard fixed targets or into collision zones.

And all this is possible because magnetic-fields exert a force on moving charges.

In fact, this is the way that a particle's charge can be determined as it passes through a strong magnetic field. Positive charges will spiral one way, negative charges spiral in the opposite way, but neutral particles are not affected, unless they decay.

When a neutral particle decays, in order to preserve electric charge, it must decay into at least two particles with equal and opposite charge. This type of decay can be seen in the presence of a strong magnetic field as two opposite spirals suddenly appearing, caused by the neutral particle decaying.

The strength of the magnetic-field can be set so that particles are bent as they travel through the field, rather than spiral and there is a relationship derived from the magnetic force exerted on the particle, qvB, which results in the centripetal force mv²/r, i.e.,

F=qvB=mv²/r

Where, F is the force acting on a particle of charge q and velocity v moving through a magnetic field with a flux density of B.

m is the rest-mass of the particle and r is the measured radius of the particle's path.

For normal velocities below light speed r = mv/qB

For velocities close to light speed r = p/qB

Where, mv is the classical momentum of the particle and p is the relativistic momentum.

This all results from considering the force between an external magnetic field and the charge on a single particle and is known as the Lorentz force.

Magnetism acting on Currents

A current is formed when many charged particles are travelling continuously in the same direction. For example, electrons carry currents in wires.

In this case an external magnetic field applied at a right angle to the current exerts a force on the wire carrying the current and this can be utilised to build a motor. In a motor, electrical energy in converted to mechanical energy to create rotation. We can consider the interaction as being between two magnetic fields, the circular loops of the current and the fixed external magnetic field.

In essence, the Lorenz force is the microscopic view of what happens to individual charges in the presence of a magnetic field whereas, the macroscopic view describes how the external magnetic field interacts with the magnetic loops of a current.

Magnetism produced by Currents in a Wire

Take a wire into which a current is being applied. The magnetic-field produced by the straight wire looks like the loops shown on the top, extreme-left, of figure 1.

Figure 1

To determine which way the magnetic flux circulates around the wire, use your right hand as shown in the inset showing the right-hand rule. Point your thumb in the direction of the current and the curl of your fingers indicates how the flux loops circulate.

Attraction and Repulsion Between two wires

Take two wires, each one with a current of 1 amp running through it and suspend the two wires so that they are close together.

If the two currents are heading in the same direction, then the wires are attracted to each other as each sits in the magnetic field produced by the other wire, creating a force of attraction.

If the two currents are heading in opposite directions, then the wires are pushed apart as each sits in the magnetic field produced by the other wire, creating a force of repulsion.

Coils

If you create a coil known as a solenoid, shown in figure 1, then all the wires at the front of the coil contain current moving from top to bottom. The current then passes under the coil and proceeds in an upward direction at the rear and towards you at the top. The point is, that all the magnetic loops being produced by all the wires combine to produce loops that exit the coil from one direction and re-enter it at the opposite end – just like the flux density output from a bar magnet!

The coil has a north and a south pole, just like the bar magnet and the magnetic flux lines look identical to those of the permanent magnet.  The big difference; if you switch off the current, the coil's magnetism vanishes.

If you insert an iron bar into the centre of the coil, you get a more powerful magnetic field.

What is the Value of B for a Coil?

Michael Faraday (1791 to 1867) performed many experiments investigating electricity and magnetism and came up with the following equation to express the magnetic flux density surrounding a current in a wire;

Where B is the magnetic flux density at a distance r from the wire, carrying a current of I amps and mu is the permeability of the medium in which the wire is placed, such as air.

For a coil, he came up with the following equation;

where n is the number of turns of wire on the coil and L is the length of the coil.

What use are coils?

Many cars rely on coils to boost the 12 volts of the car's electric system into a high voltage suitable to create a spark to ignite the petrol vapour in a cylinder.

There are actually two coils wrapped around a central core, one is the primary coil, connected to the 12 volts car system via an electronic switch.  The engine management system opens and closes this switch many times a minute, so current is constantly being switched on and off in the primary coil. As a consequence, when the magnetic field created by the primary coil suddenly collapses, it induces a massive voltage spike in the secondary coil, which has many more turns than the primary coil. 

This is magnetic induction at work created by a changing magnetic-field.

With the correct ratio of number of turns in primary coil to turns in secondary coil, this induced voltage spike can range from 15,000 volts to as much as 40,000 volts and is used to create a spark in the engine's cylinders.  The timing of all this is controlled so that the cylinders work in tandem turning the crank shaft.

So, a collapsing magnetic field induces current to flow in an attached coil and if that attached coil contains many more turns than the primary, then a high voltage is created.

This is the principle of the transformer where normally, an alternating voltage is fed to a primary coil, which is in close proximity to a secondary coil in which a second alternating voltage is induced. Depending on the number of turns on the second coil, the output can be a higher or a lower AC voltage than that on the primary.

The coils are only connected by metalware, there is no electrical connectivity involved. In this way, mains voltage of 240 volts AC can be stepped down to 5 volts AC and converted to 5 volts DC to charge your phone.

Are there other uses of coils?

There are lots of uses of coils, but the most beneficial is the use of coils in motors or in electrical generators. There is a simple difference;

Motor coils require a current flowing into the coil, operating in a strong magnetic field to create rotation of the coil to drive wheels or a propeller. In the case of the motor, the static magnetic field converts electrical energy to mechanical energy.

Generator coils must be mechanically rotated in the presence of a strong magnetic field and currents are induced in the coil. In the case of the generator, the static magnetic field converts the mechanical energy of rotation into electrical energy.

Faraday discovered all this by experimenting with single turn coils (n=1), allowed to rotate in between two magnets, one with a north-pole and the other a south pole.

The Electric Motor

Faraday's single-coil, prototype motor is illustrated in figure 2, where current flowing in the coil creates rotation. The direction of the current, the forces and the magnetic field are all shown in figure 2, together with the equation defining the maximum force on the coil when it is in the horizontal plane.

Figure 2

The single-turn coil is shown in between a north-pole and a south-pole of a single U shaped magnet or two separate magnets. Current is pumped into one side of the coil and exits out of the coil on the other side, producing a clockwise current in this situation.

Forces are created on either side of the coil, which are equal and opposite creating torque that rotates the coil clockwise as viewed along the axis of the coil.

There is a more detailed description of the single-coil DC-motor and the AC-motor in Part 3 of A Journey into Modern Physics.

The Electrical Generator

An electrical generator can either be a DC device known as a dynamo, or an AC device, known as an alternator.  Vehicles switched from using dynamos to alternators, which are more efficient, decades ago. These are used to power the vehicle's electrical systems and charge the battery when the engine is running.

Figure 3 illustrates the basic principal, where mechanical rotation of the coil creates a current in the coil, converting mechanical energy to electrical energy.

Figure 3

The output from a dynamo is known as the EMF (electromotive force) and this represents the transfer of rotational energy to an electric circuit, and EMF is measured in volts. The EMF of a dynamo is the voltage produced across the coil's outputs when the coil is made to rotate in a magnetic field and current is induced in the rotating conductor.

Clearly, the EMF must be dependent upon the rate at which the coil rotates. Slow rotation produces a low EMF, whilst fast rotation produces a higher EMF at a greater frequency.

Faraday produced a law, known as Faraday's law of magnetic induction, which states that the magnitude of the induced EMF in a conductor is directly proportional to the rate at which the magnetic flux linkage changes. This applies to any conductor moving within a static magnetic field, or any static conductor experiencing a changing magnetic field. In both situations, a current is induced in the conductor.

To learn more about electrical dynamos and generators have look at Part 3 of A Journey into Modern Physics.

How Does the Earth Generate its Magnetic Field

The solid core of the planet consists of very hot iron and nickel. The core's heat comes from primordial heat when the earth was formed, trapped inside the planet; friction as iron sank to the bottom of the molten earth after its formation, and heat given off by on-going radioactive decay.

All this pent up energy and radioactive decay acts as a powerful heat source and heats up the liquid outer core, which consists of ions of iron and nickel. This heating creates convection currents that start to flow upwards in the outer core. This is known as the geodynamo, the earth's magnetic-field generator, illustrated in figure 4.

Figure 4

Where you have positive ions rising in the outer core, you have currents, big currents and as they rise, they cool and eventually start a down-ward journey back towards the molten core, where they are heated up again.

This endless movement of streams of ions upwards and then downwards creates the magnetic-field that spans out into space as illustrated in the above diagram.

The following, simple cross-section of the earth indicates the sizes of the core and outer core.

Note that the north and south poles of the earth's magnetic field are offset from the geographic north and south poles by an angle that can vary from year to year and in the past has even flipped round to the other pole. This angle has to be taken into account when converting compass readings to true north-south readings for reading maps.

The magnetic-field produced by the  geodynamo is known as the magnetosphere.

How Does the Magnetosphere Protect the Earth?

The solar wind bombards the earth constantly and in particular during solar flares pointing at the earth, when the number of particles travelling towards the planet can be immense and arrive in a matter of hours, causing widespread mayhem to the electronics in orbiting satellites.

Figure 5  shows how the magnetosphere deflects the majority of the solar wind around the earth, safely protecting the planet.

Figure 5

Without the magnetosphere, earth would have lost its atmosphere eons ago.  Remember that the solar wind particles are surrounded by magnetic-field loops that can clash with the earth's magnetic field. Where the two sets of field lines meet, they constantly re-configure themselves, squashing the earth's field on the daylight side and stretching it away on the dark side.

Solar flares are caused when the magnetic-field loops of the ion currents rising in the sun's convection currents, get tangled up creating immense magnetic stress under the sun's surface. This sometimes results in quantities of the sun's mass being catapulted out of the star as the magnetic-field lines re-order themselves into less stress-full configurations. This causes the solar wind and when the flare releases particles in the direction of the earth, the magnetosphere protects the planet.

The particles making up the solar wind can be a mixture of mainly protons (hydrogen nuclei), alpha particles (helium nuclei) and electrons.

Under certain conditions, these particles can get channeled down through gaps in the earth's magnetosphere in rings around the two poles. When this happens, the energetic solar particles actually collide with atoms in the upper and lower atmosphere and create the auroras.

You can read more about the earth's magnetosphere and the auroras in Part 3 of A Journey into Modern Physics.

Key Takeaways - Magnetism from Moving Charges

1) If a charged particle is observed as being stationary, only a static electric field is detected.

2) If a charge is observed to be in notion, then an electric field and a magnetic-field are detected.

3) This type of magnetism is only observed through motion of the observer, or the charge, or both and is therefore a relativistic effect.

4) Where currents are observed, this relativistic effect creates closed, magnetic-field loops around the moving charges.

5) When magnetic-field lines clash with other field-lines, a less stress-full configuration can be achieved when the magnetic-field lines combine and restructure themselves. This happens when the magnetic loops of the solar wind meet the earth's magnetosphere.

6) Static magnetic fields exert a force on moving charges, which can be used to bend charged particles.

7) Static magnetic fields exert a force on currents in conductors which can be used to create mechanical motion in the coils of an electric motor.

8) Mechanical motion of a coil in a static magnetic-field induces currents in the coil of an electricity generator.

9) Changing magnetic-fields can induce currents in static conductors.

10) Static magnetic-fields can induce currents in moving conductors.

11) The magnetic field produced by a constant current in a coil is similar to that produced by a bar magnet.

12) A changing magnetic field in a primary coil can induce a current in a secondary coil where the ratio of turns of the two coils governs the magnitude of the voltage across the secondary coil.

13) A bar magnet's magnetic field is stronger than the earth's magnetic field on the surface of the planet, but only close to the bar magnet and drops off according to the inverse cube of distance falling to 0 just a short distance from the bar magnet.

14) The earth's magnetic-field can be detected at all points across the planet and because it extends out into space, it has saved the planet from bio-extinction.

© 2026 Kieron Conway - All rights reserved.

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