Measuring and calculating EMFs

It is quite easy to measure magnetic fields.  Instruments are usually based on search coils (though other types exist as well) and can be small and handheld, or larger and more sophisticated.  Measuring electric fields is possible too but harder because the person making the measurement often perturbs the field. Calculations of EMFs are also easy for sources (like overhead lines and underground cables) that have clearly defined geometries.

measuring fields - simple version

Measurement of electric and magnetic fields

This is a summary of instruments for measuring fields. A more detailed technical description of the issues is also available in the next toggle below.

The first commercial instruments designed specifically for measuring power-frequency fields became available in the 1980s. There are now many instruments available, which vary in the number of axes they measure, how sophisticated the electronics are, whether they record fields, and whether they are meant for survey use or as a personal monitor.

There is no “correct” or “best” meter. The best meter to use depends on the purpose it is to be used for.

Measuring magnetic fields


There are three different sensors widely used for measuring magnetic fields: search coils, fluxgate magnetometers, and Hall-effect devices.

photo of Emdex metersMost practical instruments for power frequencies use search coils, either a single coil or three orthogonal coils. The coils themselves can either be made as small as possible, for use in personal exposure meters where size and weight are important criteria, or they can be larger, often 0.1 m across, to increase sensitivity and provide some spatial averaging.

Measuring electric fields


photo of Holaday meterMeters for electric fields usually use as sensors two parallel conducting plates. Alternative sensors, e.g. based on rotation of polarised light, are less common.

Three-axis electric-field meters are available, but single-axis meters are more common.

A person holding an electric-field meter would perturb the field. To measure the unperturbed field, the meter is usually held at the end of a long non-conductive horizontal rod or a vertical tripod. This can reduce perturbation to acceptable levels, but care is still needed to get accurate readings. More on how to do accurate readings

Personal exposure meters do exist for electric fields. However, wearing a meter on the body perturbs the electric field being measured in unpredictable ways.

measuring fields - more technical version

Measurement of electric and magnetic fields

 This is a fairly technical account of measurement principles - for a simpler version see the previous toggle.

The first commercial instruments designed specifically for measuring power-frequency fields became available in the 1980s. There are now many instruments available, which vary in various characteristics:

(a) Number of axes of detection. There are no sensors that directly assess a resultant field in a random direction in space; sensors generally measure the field in one direction. A meter may have one sensor. If this is aligned by the user with the direction of maximum field it will give a reading of the maximum field in a single direction; the overall resultant field may be between 1.0 and 1.41 times this value depending on the degree of polarisation. If the meter has three orthogonal sensors, the resultant field can be obtained from the three values measured by root-sum-of-squares addition: Resultant = (X2+Y2+Z2)1/2 .

This resultant value is independent of the orientation of the meter, vastly simplifying use of the meter.
More on elliptically polarised fields
   
(b) Measure of field. Various measures of a sine wave are possible, e.g. peak, rectified average, root-mean-square (rms). For a single frequency, i.e. a pure sine wave, these can be scaled to give the same result, but in the presence of harmonics they can differ considerably. In the absence of a known biophysical mechanism, there is no conclusive basis for asserting that any one measure is correct. However, by analogy with other areas of measurement science, there is an assumption that rms is the preferred measure. Some meters capture the actual waveform for future analysis.
   
(c) Frequency response. Instruments may be sensitive to a single frequency e.g. 50 Hz or 60 Hz or to a range of frequencies. If sensitive to a range of frequencies, the response may be flat or may be proportional to frequency. A flat frequency response between 20 or 30 Hz and a few kiloherz is generally regarded as suitable for many general purpose measurements.
   
(d) Size of sensors. Sensors can be made small – a few millimetres - and therefore capable of investigating variations of field over small distances. However, there may also be times when it is desirable to use larger sensors which measure the average field over their area. Here are two different ways of making a magnetic-field instrument:

 photo of search coil cube    photo of coils inside Emdex meter

The sensor on the left has the three coils centred on each other.  They are air-cored, and to get the necessary sensitivity, they have thousands of turns of wire.  These examples are 10 cm square.

The sensor on the right has much smaller coils to make a smaller overall meter.  To get the sensitivity despite the smaller size, the coils have iron cores.  This means they cannot be centred on the same point; they are arranged separately, at right angles to each other (two are flat on the pcb at the bottom left, the third, vertical, coil is provided with a white mechanical support at the bottom right).

    
(e) Readout and logging. Meters may have analogue or digital displays. They may only display a value in real time, or they may be capable of logging values with various degrees of sophistication, and of calculating various parameters of the field such as averages or maxima.
   
Given the variations in facilities provided by a meter, there is an inevitable variation in size, weight, and battery consumption. Some meters are most suitable for detailed surveys by experts; others are small and light enough to be worn by volunteers for extended periods.

There is no “correct” or “best” meter. The best meter to use depends on the purpose it is to be used for.

Measuring magnetic fields

There are three different sensors widely used for measuring magnetic fields:
 
(a) Search coils. The simplest meters measure the voltage induced in a coil of wire. For a sinusoidally varying magnetic field, B, of frequency f, the voltage, V, induced in the coil is given by:

V=-2 π f B 0A cos(ω t)

where ω = 2 π f is the frequency of the field and  A is the area of the loop, and  B0 is the component of B perpendicular to the loop.

The voltage induced by a given field increases with the addition of more turns of wire or of a ferromagnetic core - see the examples above. To prevent interference from electric fields, the magnetic field probe must be shielded. If the meter is used for surveys or personal exposure measurements, frequencies lower than approximately 30 Hz must be filtered out to remove voltages induced in the probe by the motion of the meter in the earth’s magnetic field.
   
(b) Fluxgate magnetometers. These detect a magnetic field by the asymmetry it produces in a ferromagnetic material deliberately driven in magnetic saturation alternately in opposite directions at a high frequency.
   
(c) Hall-effect devices. The sensor is designed to measure the transverse Hall voltage across a thin strip of semiconducting material carrying a longitudinal current.

Most practical instruments for power frequencies use search coils, either a single coil or three orthogonal coils. The coils themselves can either be made as small as possible, with a ferromagnetic core to increase sensitivity, for use in personal exposure meters where size and weight are important criteria; or they can be larger, often 0.1 m across, to increase sensitivity and provide some spatial averaging. Fluxgate magnetometers cannot be made as small or as cheap, but have the advantage of responding to dc fields as well as ac. Hall devices are little used as their resolution is poorer and they suffer from drift but have uses at higher fields.

Measuring electric fields

Meters for electric fields usually use as sensors two parallel conducting plates. Alternative sensors, e.g. based on rotation of polarised light, are less common.

Three-axis electric-field meters are available, but single-axis meters are more common. This is partly because it is harder to make three-axis meters for electric fields than for magnetic fields, and partly because in one common measuring situation, near ground underneath or close to overhead power lines, the electric field is linearly polarised and in a known direction (vertical), and therefore a single-axis meter is perfectly sufficient.

A person holding an electric-field meter would perturb the field. To measure the unperturbed field, the meter is usually suspended at the end of a long non-conductive horizontal rod or vertical tripod. The reading is read from a distance on a suitably sized display, recorded within the meter for later analysis, or transmitted to a readout device by fibre-optic. This can reduce perturbation to acceptable levels. However, given the ease of perturbation of electric fields, it is easy to make erroneous measurements, particularly when there is:

  • extremes of temperature and humidity;
  • insufficient distance of the probe from the investigator;
  • instability in meter position;
  • loss of non-conductive properties of the supporting rod.

Electric fields can also be measured at fixed locations, e.g. under transmission lines or in laboratory exposure chambers by measuring the current collected by a flat conducting plate placed at ground level. For sinusoidal fields, the electric flux density can be calculated from the area of the plate (A), the permittivity of a vacuum , the frequency (f) and the measured current induced in the plate  in the expression below:

E=Irms/2πfε0A

Personal exposure meters do exist for electric fields. However, wearing a meter on the body, perturbs the electric field being measured in unpredictable ways. Typically, where exposure to electric fields of large groups of subjects is being measured, a meter is placed in an armband, shirt pocket or belt pouch. Perturbation of the ambient field by the body precludes obtaining an absolute value of the field and, at best, the average value of such measurements reflects the relative level of exposure.

Calculating fields

Calculating electric and magnetic fields

If you know that there is one dominant source of EMFs present it is often possible to calculate the fields it produces.  Overhead lines and underground cables lend themselves to this.  It is possible for substations too, but harder because the geometry is more complicated.  You can't easily do calculations for low-voltage distribution sources because you don't normally know the currents accurately enough. 

Download a step-by-step tutorial on how you would go about calculating the magnetic field from a simple three-phase circuit: How to calculate the magnetic field.pdf.

Calculations are often preferable to measurements because you can perform them for any desired conditions rather than being limited to the particular conditions at the time you do the measurement.

Calculations can be as accurate as you like.  You can see a comparison of calculations and measurements from an overhead line and here for a discussion of how accurate the calculations can be

Calculations (and measurements) are often performed at 1 m above ground because this is the relevant height for assessing the induced current in a person.

For power lines and cables, calculations usually assume the conductors are infinite straight lines.  But see details of the effect that modelling the sag of the conductors has (usually quite a small effect, which is why it's not usually done) and see what happens when the conductors are only finite length.

We offer an on-line calculator for the magnetic fields from some of the standard UK overhead lines.

Commercial measurement and calculation services

We don't recommend particular commercuial providers but we do list some possibilities.