The engineering design of electromagnets is systematized by means of the concept of the magnetic circuit. In the magnetic circuit a magnetomotive force F, or Fm, is defined as the ampere-turns of the coil that generates the magnetic field to produce the magnetic flux in the circuit. Thus, if a coil of n turns per metre carries a current i amperes, the field inside the coil is ni amperes per metre and the magnetomotive force that it generates is nil ampere-turns, where l is the length of the coil. More conveniently, the magnetomotive force is Ni, where N is the total number of turns in the coil. The magnetic flux density B is the equivalent, in the magnetic circuit, of the current density in an electric circuit. In the magnetic circuit the magnetic equivalent to current is the total flux symbolized by the Greek letter phi, ϕ, given by BA, where A is the cross-sectional area of the magnetic circuit. In an electric circuit the electromotive force (E) is related to the current, i, in the circuit by E = Ri, where R is the resistance of the circuit. In the magnetic circuit F = rϕ, where r is the reluctance of the magnetic circuit and is equivalent to resistance in the electric circuit. Reluctance is obtained by dividing the length of the magnetic path l by the permeability times the cross-sectional area A; thus r = l/μA, the Greek letter mu, μ, symbolizing the permeability of the medium forming the magnetic circuit. The units of reluctance are ampere-turns per weber. These concepts can be employed to calculate the reluctance of a magnetic circuit and thus the current required through a coil to force the desired flux through this circuit.

Several assumptions involved in this type of calculation, however, make it at best only an approximate guide to design. The effect of a permeable medium on a magnetic field can be visualized as being to crowd the magnetic lines of force into itself. Conversely, the lines of force passing from a region of high to one of low permeability tend to spread out, and this occurrence will take place at an air gap. Thus the flux density, which is proportional to the number of lines of force per unit area, will be reduced in the air gap by the lines bulging out, or fringing, at the sides of the gap. This effect will increase for longer gaps; rough corrections can be made for taking the fringing effect into account.

It has also been assumed that the magnetic field is entirely confined within the coil. In fact, there is always a certain amount of leakage flux, represented by magnetic lines of force around the outside of the coil, which does not contribute to the magnetization of the core. The leakage flux is generally small if the permeability of the magnetic core is relatively high.

In practice, the permeability of a magnetic material is a function of the flux density in it. Thus, the calculation can only be done for a real material if the actual magnetization curve, or, more usefully, a graph of μ against B, is available.

Finally, the design assumes that the magnetic core is not magnetized to saturation. If it were, the flux density could not be increased in the air gap in this design, no matter how much current were passed through the coil. These concepts are expanded further in following sections on specific devices.

Design Of Large Electromagnets.

Sooner or later almost every scientific research laboratory finds that it requires a facility for producing large magnetic fields. A number of advanced technologies likewise require large electromagnets. A cyclotron, for example, is a device used for scientific research in which subatomic charged particles are accelerated by an alternating electric field in a constant magnetic field. It uses a large magnet to produce moderate fields but with a pole diameter that may be several metres. Some industries make use of huge, high-powered electromagnets for lifting purposes.

The basic design principles of large electromagnets are those discussed earlier. The difficulties arise in trying to estimate the magnitude of the fringing flux across the air gap and the leakage flux around the coils. Their effects are minimized by using a tapered shape for the cores and pole caps; a typical laboratory magnet is shown in Figure 4. Because soft iron saturates at 2.16 webers per square m, flux densities in the air gap are generally limited to the region of 2.1 webers per square m with iron magnets.

When designed for lifting or load-carrying purposes, an electromagnet may be required to have a single exposed pole face to which the load to be carried will attach itself, and it will therefore have the shape of a bar magnet. The design is then dominated by the demagnetizing field. Suitably designed magnets can lift many times their own weight and are in general use in steelworks and scrapyards.