Electromagnet:

An electromagnet is a type of magnet in which the magnetic field is produced by the flow of an electric current. The magnetic field disappears when the current ceases.

Invention and history

British scientist William Sturgeon invented the electromagnet in 1823.^[1]^[2] The first electromagnet was a horseshoe-shaped piece of varnished iron that was wrapped with 18 turns of bare copper wire (insulated wire didn't exist yet). When a current was passed through the coil, the iron became magnetized and when the current was stopped, it was de-magnetized. Sturgeon displayed its power by showing that although it only weighed seven ounces, it could lift nine pounds when the current of a single-cell battery was applied. Beginning in 1827, American scientist Joseph Henry systematically investigated and improved the electromagnet.^[3] By using wire insulated by silk thread he was able to wind multiple layers of wire on cores, creating powerful magnets with hundreds of turns of wire, including one that could support 2063 pounds.

Introduction

The most fundamental type of electromagnet is a simple segment of wire (see figure). The amount of magnetic field generated depends upon the amount of electrical current that flows through the wire. In order to concentrate the magnetic field generated by a wire, it is commonly wound into a coil, where many segments of wire sit side by side. A coil forming the shape of a straight tube, a helix (similar to a corkscrew) is called a solenoid; a solenoid that is bent into a donut shape so that the ends meet is a toroid. Much stronger magnetic fields can be produced if a "core" of ferromagnetic material (commonly soft iron) is placed inside the coil. The core concentrates the magnetic field that can then be much stronger than that of the coil itself.

Magnetic fields caused by coils of wire follow a form of the right-hand rule.^[4]^[5]^[6]^[7]^[8]^[9] If the fingers of the right hand are curled around the coil in the direction of current flow (conventional current, flow of positive charge) through the windings, the thumb points in the direction of the field inside the coil. The side of the magnet that the field lines emerge from is defined to be the north pole.

Electromagnets and permanent magnets

The main advantage of an electromagnet over a permanent magnet is that the magnetic field can be rapidly manipulated over a wide range by controlling the amount of electric current. However, a continuous supply of electrical energy is required to maintain the field.

As a current is passed through the coil, small magnetic regions within the material, called magnetic domains, align with the applied field, causing the magnetic field strength to increase. As the current is increased, all of the domains eventually become aligned, a condition called saturation. Once the core becomes saturated, a further increase in current will only cause a relatively minor increase in the magnetic field. In some materials, some of the domains may realign themselves. In this case, part of the original magnetic field will persist even after power is removed, causing the core to behave as a permanent magnet. This phenomenon, called remanent magnetism, is due to the hysteresis of the material. Applying a decreasing AC current to the coil, removing the core and hitting it, or heating it above its Curie point will reorient the domains, causing the residual field to weaken or disappear.

In applications where a variable magnetic field is not required, permanent magnets are generally superior. Additionally, permanent magnets can be manufactured to produce stronger fields than electromagnets of similar size.

Design of electromagnets

The magnetic field of electromagnets in the general case is given by Ampere's Law:

which says that the integral of the magnetizing field H around any closed loop of the field is equal to the sum of the current flowing through the loop. Computing the magnetic field and force exerted by ferromagnetic materials is difficult for two reasons. First, because the geometry of the field is complicated, particularly outside the core and in air gaps, where fringing fields and leakage flux must be considered. Second, because the magnetic field B and force are nonlinear functions of the current, depending on the nonlinear relation between B and H for the particular core material used. For precise calculations the finite element method is used.

However, in designing a DC electromagnet, in which the current is either on or off, the relations can be simplified. The main feature of ferromagnetic materials is that the B field saturates at a certain value, which is around 1.6 T for most high permeability core steels. The B field increases quickly with increasing current up to that value, but above that value the field levels off and increases at the much smaller paramagnetic value, regardless of how much current is sent through the windings. So it is not possible to obtain a much stronger magnetic field from an electromagnet than 1.6 T. Inside the core, the magnetic field is approximately uniform. If the magnetic circuit is only broken by air gaps small compared to the cross sectional area of the core, the B field in the gap is approximately the same as in the core.

Force exerted by magnetic field

When the magnetic field path is entirely in high permeability material (no air gaps), the maximum force exerted by an electomagnet is:

Where $\mu_0 = 4 \pi (10^{-7})\,$ Newton Ampere^-2. So saturation sets a limit on the maximum force per unit core area, or pressure, an electromagnet can exert; roughly:

Given a core geometry, the B field needed for a given force can be calculated from (1); if it comes out to much more than 1.6 T, a larger core must be used.

Magnetic field created by a current

Once the B field needed is known, the magnetomotive force, the current multiplied by the number of turns in the winding $NI\,$ , in Ampere-turns, can be calculated. For an electromagnet with a single magnetic circuit, of which length $L_{core}\,$ is in the core material and length $L_{gap}\,$ is in air gaps, Ampere's Law reduces to:^[10]^[11]

This is a nonlinear equation, because the permeability of the core, $\mu\,$ is a function of the magnetic field. For an exact solution, the value of $\mu\,$ at the B value used must be obtained from the core material hysteresis curve. If B is unknown, the equation must be solved by numerical methods. However, if the magnetomotive force is well above saturation, so the core material is in saturation, the magnetic field won't vary much with changes in $NI\,$ anyway. For a closed magnetic circuit (no air gap) this occurs at a magnetomotive force of approximately 787 Ampere-turns per meter of flux path.

For most core materials, $\mu_r = \mu / \mu_0 \approx 2000 - 6000\,$ .^[11] So in equation (2) above, the second term dominates. Therefore, in magnetic circuits with an air gap, the behavior of the magnet depends strongly on the length of the air gap, and the length of the flux path in the core doesn't matter much.

Closed magnetic circuit

It can be seen that to maximise the force, a short flux path with a wide cross sectional area is preferred. To achieve this, in applications like lifting magnets (see photo above) and loudspeakers a flat cylindrical design is often used. The winding is wrapped around a short wide cylindrical core that forms one pole, and a thick metal housing that wraps around the outside of the windings forms the other pole.

Force between electromagnets

Superconducting electromagnets

When a magnetic field higher than the ferromagnetic electromagnet limit of 1.6 T is needed, superconducting electromagnets can be used. Instead of using ferromagnetic materials, these use superconducting windings cooled with liquid helium, which conduct current without electrical resistance. These allow enormous currents to flow, which can generate large magnetic fields. Superconducting magnets are so far limited to fields of 15-20 T. The necessary refrigeration equipment and cryostat make them much more expensive than ordinary electromagnets. However, in high power applications this can be offset by lower operating costs, since after startup no power is required for the windings, since no energy is lost to ohmic heating. They are used in particle accelerators, MRI machines, and research.

Use of electromagnets