Electric and magnetic fields

The electric field is generated by the presence of electric charges. Let’s take the example of the balloon charged with static electricity that our observant readers discovered in the “Basic electricity” section:

The electric field intensity depends on the difference of potential between the two charged areas and on the distance separating them. An approximation of the electric field between two parallel flat surfaces is given by the following formula (assuming a uniform field in space):

There is a natural electric field at the surface of the Earth. It is generated by the difference of potential between the high atmosphere (the positively charged ionosphere) and the Earth (negatively charged).

Electric charges continuously leave the Earth surface towards the atmosphere. The thousands of electric (*) storms that occur every day at the four corners of the planet ensure, via lightning, the return of these charges to the ground in order to maintain a global equilibrium and keep life on Earth possible.

Lightning is preferentially attracted by elevated and/or pointed objects because the electric field (and therefore the force applied to the charges) is more intense in their proximity than in the surrounding: it’s the “point effect”.

The electric charges have a tendency to concentrate on the pointed parts of a conductor, typically a smaller area. Therefore, the intensity of the electrical forces is very high. The strong electric field that they generate causes the ionisation of the air and thus increases the conductivity of the air. For example, a pointed object like a lightning conductor doesn’t actually attract lightning, but it makes more likely, during a storm, because of the point effect, the formation of discharges (e.g. St. Elmo’s fires at the top of boat masts).

The point effect is also responsible for corona discharges, a phenomenon that takes place, among others, around overhead power lines in certain conditions.

The presence of small protuberances on the surface of conductors, such as a drop of water or snow flakes, or even an insect, cause large increases of the electric field. The corona effect varies drastically in function of the conditions of the external surface and of the atmosphere.
(Source : “Transport et distribution de l’énergie électrique” on the Université de Liège website)

If our eyes were capable of visualising electric and magnetic fields, here is what we would see when looking at an unlit flashlight and a toaster: a static electric field around the flashlight and alternating at 50 Hz surrounding the toaster.

The darker areas represent zones of higher intensity of the fields.

There is also a magnetic field around the earth. It can be detected by observing a compass needle. It is thought to be produced by movements of the molten magma in the earth’s core.

Earth’s magnetic field plays a critical role in the protection of the planet by deflecting cosmic radiation and solar winds particles. This deflection takes place in the magnetosphere (the atmosphere layer above the ionosphere, more than 1000 km above earth’s surface). Auroras borealis (at the North pole) and auroras australis (at the South pole) are caused by the collision of high energy particles and the magnetosphere.

A magnetic field is produced by moving electric charges. This motion takes different forms according to the type of materials and their use:

The magnetic North pole is defined as the location where the magnetic field lines are perpendicular to the surface of the earth. The geographic North pole, for its part, is defined by earth’s rotation axis. The magnetic field axis is not aligned with earth’s rotation axis, and as a result the magnetic North is actually about 1000 km away from the geographic North (for the moment).

The orientation of the magnetic field lines depends on the configuration of the magnetic field source. Let’s look at two examples:

1. Around a current carrying straight wire, the magnetic field lines are circular.

2. Around a coil that is carrying a current, the magnetic field lines look like those of a magnet.

By analogy, the coil is said to have a north pole where the lines exit and a south pole where they enter.

The magnetic field at a point P depends on the current and on the distance to the conductor. It is denoted H and is measured in ampere/metre (A/m).

The direction of the magnetic field lines can be determined by the “right hand grip rule”: when the thumb points to the direction of the current (convention + towards –), the magnetic field orientation is that of the folded fingers.

The magnetic field H (in A/m) is frequently expressed by its magnetic induction B (in tesla, T). In a given material, the magnetic field and the magnetic induction are linked by the following equation:

The magnetic permeability of a material is its ability to concentrate the magnetic flux lines and thus increase the magnetic induction. Therefore the magnetic induction depends on the medium where it is produced (see the site glossary under “Magnetic permeability”).

The magnetic permeability of air is 4 π .10^-7 H/m.

Therefore, in a vacuum or in air, a 1 A/m H-field is associated to a 1,26 µT B-field.

Note:

• The former unit of magnetic induction, the gauss (G), is still regularly used in some regions. The conversion is as follows: 10-4 T = 1 G or, to use values more commonly encountered in a 50/60 Hz environment: 0.1 µT = 1 mG.
• Later in this module we may often use “magnetic field” for B or B-field which is measured in μT.

If our eyes were capable of visualising electric and magnetic fields, here is what we would see when looking at a flashlight and a toaster when they are turned on: static electric and magnetic fields around the flashlight and alternating at 50 Hz surrounding the toaster.

The darker areas represent zones of higher intensity of the fields.

Both electric and magnetic fields decrease rapidly when moving away from the source.

Depending on the source, the decrease may be more or less rapid:

In the surroundings of an electrical cable (e.g. a cable from a high voltage powerline), the field intensity is inversely proportional to the distance (in our jargon, we use the notation 1/r). In the surroundings of domestic cables (“round-trip” conductors), the field intensity decreases with the square of the distance (1/r²) and near a coil, as for example an industrial induction furnace, with the cube of the distance (1/r³).

Electric alarm clocks, bedside lamps and most household appliances can be considered as sources from which magnetic field intensity decreases with the square of the distance. In concrete terms, this means that when the distance doubles, field intensity decreases by a factor of 4. For example, if the magnetic field intensity is 1 microTesla at 30 cm from an electric alarm clock, the intensity will become 0.25 µT at 60 cm, 0.0625 at 120 cm, and so on.

Further information regarding electric and magnetic fields values is available in the module “Fields in our environment”.

Example of an electric cord supplying a lamp with a 100 watts light bulb at 230 V:

1. Measuring the voltage between the two conductors in the cable (with a voltmeter), we obtain approximately 230 V (effective value, 50 Hz sinusoidal)

2. If the lamp is turned on, we can measure (with an ammeter) the current in the cable conductors (identical in both conductors, but in reverse directions):

P (in W) = V (in V). I (in A)

100 = 230 . I
then I = 0.435 A (effective value, 50 Hz sinusoidal)

3. Calculation of the magnetic field near the electric cord:

• Assuming a single conductor (effective value, 50 Hz sinusoidal):

approximately 0.8 µT at 10 cm

• With both conductors together (round-trip conductors):

approximately 0.017 µT at 10 cm, that is 47 times less than in the fictitious single conductor.

We can derive the magnetic field values in function of the distance from the cables:

The magnetic field varies with the inverse of the square of the distance (1/r²) as shown earlier. It would then require a load consuming more than 10 A to reach a B field higher than 0.4 µT at 10 cm from the cables and that value would decrease by a factor of 10 (which means 0.04 µT) at 31 cm from the cables.

Various commercial instruments exist to measure electric and/or magnetic fields:

• Electric field measurements require some important precautions, as it is influenced by nearby objects as well as by the presence of the operator. One must take the measurement away from objects and people, at the end of an insulated long pole for example.
• Alternating magnetic B-fields (here 50 Hz) is measured by means of three orthogonal solenoids. The inducted voltage in each of the solenoids gives the 3 components (x, y, and z) of the field.

At very low frequencies, the magnetic field is not disturbed by the presence of objects or people, so its measurement doesn’t require the same precautions than the electric field. It can easily be measured by a dosimeter worn on someone’s belt for long term exposure situations.

So far, we concerned ourselves with static fields (magnets) and 50 Hz alternating fields generated by the power network. Among variable fields, 50 Hz fields are only a minute part of the electromagnetic waves spectrum: among others, visible light, radio waves, and X-rays are also part of that spectrum.

Gamma rays and cosmic rays are the most energetic of all.

The level of exposure to cosmic radiation increases with altitude, as there is less atmosphere to protect us; air travel is the source of most of our exposure.

The electromagnetic spectrum covers a very wide range of frequencies (in Hz) and wavelengths (in m).

The frequency is the number of cycles per second. The unit of frequency is the hertz (Hz). The alternating current power supply of most electrical appliances is at a 50 Hz frequency. The fields it produces are also alternating at 50 Hz.

The wavelength is the distance travelled between two consecutive cycles of the wave.

Frequency and wavelength are related: the higher the frequency, the shorter the wavelength. The speed of propagation of electromagnetic waves is the speed of light in vacuum, air, and other gases, that is a speed of about 300,000,000 m/s.

Therefore, at a 50 Hz frequency for example, the wave travels 6000 km in one second.

Waves can also differ in their shape. We have so far described sinusoidal (*) waves, but there are square waves, pulse waves, etc.

Electromagnetic waves are a form of energy. The amount of energy carried by a wave depends on its frequency (or its wavelength). Radiations whose frequency is:

1. Higher than 10¹⁵ Hz contain enough energy to break chemical bonds and ionise molecules. They are said to be ionising radiations: cosmic rays, gamma rays and X rays. In the human body, the ionisation energy level for water is between 12 and 35 eV (electron-volt). For a radiation to have such high energy, the frequency must be higher than 3.10¹⁵ Hz, that is approximately that of UV radiation.

Source: ISSep, 2001

2. Lower than 10¹⁵ Hz are not sufficiently energetic to break chemical bonds. They are said to be non-ionising: most UV radiation, visible light, radio frequencies and low and extremely low frequencies. UV rays are at the threshold of ionisation.

Note: Non-ionising radiations still carry quite a bit of energy: it is that energy that heats your lunch in a microwave oven or that gives you that sun burn instead of the nice tan you were looking for…

Different frequencies radiations are produced by different processes. For further information, see Sources of electromagnetic waves.

At the beginning of this module, we introduced electric and magnetic fields separately. Later, we spoke of the electromagnetic waves spectrum. Why?

In fact, time-varying fields are, when sufficiently far from the source, waves that spread at the speed of light. However, the transmitters of these waves have for output either a mostly electric or mostly magnetic field depending on their geometry and their operating principle. These fields are labelled near electric or near magnetic fields; strictly speaking, there is no propagation.

Further away from the source, time-varying fields evolve: the magnetic field progressively increases in relation with the electric field (or vice versa), so that at a “long” distance from the transmitter (*), the electric and magnetic components become intertwined and propagate as a wave, perpendicular to each other and perpendicular to the direction of propagation. We are now in the domain of far electromagnetic fields.

Note: At 50 Hz, we are always in near field. There is no propagation to speak of, thus we must consider electric and magnetic fields independently.

Electromagnetic radiation can be produced by various processes:

• The first process involves electrons transitioning from one given energy level to a lower energy level. The energy difference is converted to light. These transitions can take place inside atoms, molecules, or solids. For example, in a fluorescent tube, light is produced by electronic transitions in the atoms of the gas that fills the tube (actually, they first produce UV radiation that causes the phosphorescent material coating the tube to emit visible light). In an LED (light emitting diode), which is an electroluminescent semiconductor, the light is produced by electronic transitions in the semiconductor material, essentially between the conduction and valence bands.
• A second process is the acceleration (or deceleration) of charged particles. This process is the operating principle of a radio or Wifi transmitter: a variable current travels through the antenna, which means that a variable acceleration is imparted to the charges that are the current.
• Last, very high energy electromagnetic waves (including gamma rays) are produced by energy transitions inside the atom nucleus, by interaction of subatomic particles, or by the annihilation of matter by antimatter. Such waves are observed in high energy colliders (such the CERN in Geneva), in the sun, and in deep space.

Electric storms are associated with a particular type of cloud: the cumulonimbus, the top of which can be culminating at 12 000 metres or more above earth’s surface. Negative charges accumulate at the bottom of the cumulonimbus, positive charges at the top (*).

The presence of negative charges at the bottom of the cloud leads to an accumulation of positive charges on the ground. The electric field between the base of the cloud and the ground reverses itself and becomes stronger.

The phenomenon known as lightning is highly susceptible to the very intense electric field. Lightning takes place in three steps: (1) creation of an ionised channel by a downward stepped leader (it makes it way down by steps of tens of metres) starting at the base of the cloud, (2) when this leader gets close enough to the ground, an upwards streamer (similar to a leader, but made of positive charges) starts from the ground, (3) leader and streamer connect, forming a conducting channel between earth and the cloud. The electric current through that channel is the major discharge, that we call the lightning strike.