Definitions

# electromagnet

[ih-lek-troh-mag-nit]
electromagnet, device in which magnetism is produced by an electric current. Any electric current produces a magnetic field, but the field near an ordinary straight conductor is rarely strong enough to be of practical use. A strong field can be produced if an insulated wire is wrapped around a soft iron core and a current passed through the wire. The strength of the magnetic field produced by such an electromagnet depends on the number of coils of wire, the magnitude of the current, and the magnetic permeability of the core material; a strong field can be produced from a small current if a large number of turns of wire are used. Unlike the materials from which permanent magnets are made, the soft iron in the core of an electromagnet retains little of the magnetism induced in it by the current after the current has been turned off. This property makes it more useful than a permanent magnet in many applications. Electromagnets are used to lift large masses of magnetic materials, such as scrap iron. They are essential to the design of the electric generator and electric motor and are also employed in doorbells, circuit breakers, television receivers, loudspeakers, atomic particle accelerators, and electromagnetic brakes and clutches. Electromagnetic propulsion systems can provide motive power for spacecraft. Electromagnets are also essential to magnetic levitation systems. Such systems often use a special kind of electromagnet whose coil is made of a superconducting metal. Because the coils of a superconducting electromagnet offers no resistance to the flow of electricity, no energy is wasted by the development of heat, and the magnetic field produced by the magnet can be very strong. Superconducting magnets are used in magnetic-resonance imaging, and can also be used for energy storage. The first practical electromagnet was invented early in the 19th cent. by William Sturgeon.

Device consisting of a core of magnetic material such as iron, surrounded by a coil through which an electric current is passed to magnetize the core. When the current is stopped, the core is no longer magnetized. Electromagnets are particularly useful wherever controllable magnets are required, as in devices in which the magnetic field is to be varied, reversed, or switched on and off. Suitably designed magnets can lift many times their own weight and are used in steelworks and scrap yards to lift loads of metal. Other devices that utilize electromagnets include particle accelerators, telephone receivers, loudspeakers, and televisions.

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

Danish scientist Hans Christian Ørsted discovered in 1820 that electric currents create magnetic fields. British scientist William Sturgeon invented the electromagnet in 1823. His first electromagnet was a horseshoe-shaped piece of varnished iron that was wrapped with about 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. However, Sturgeon's magnets were weak because the uninsulated wire he used could only be wrapped in a single layer around the core, limiting the number of turns. Beginning in 1827, American scientist Joseph Henry systematically improved and popularized the electromagnet. 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

A wire with an electric current passing through it generates a magnetic field around it(see figure), this is a simple electromagnet. The strength of magnetic field generated is proportional to the amount of current.

In order to concentrate the magnetic field generated by a wire, it is commonly wound into a coil, where many turns of wire sit side by side. The magnetic field of all the turns of wire passes through the center of the coil. 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, such as soft iron, is placed inside the coil. The core magnifies the magnetic field to thousands of times the strength of the field of the coil alone. This is called a ferromagnetic-core or iron-core electromagnet.

The direction of the magnetic field through a coil of wire can be found from a form of the right-hand rule. 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.

## Design of ferromagnetic electromagnets

For definitions of the variables below, see box at end of article.

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

$int mathbf\left\{J\right\}cdot dmathbf\left\{A\right\} = oint mathbf\left\{H\right\}cdot dmathbf\left\{l\right\}$

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 the strength of the magnetic field possible from an iron core electromagnet is limited to 1.6-2 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.

### Magnetic field created by a current

The magnetic field created by an electromagnet is proportional to both the number of turns in the winding, $N,$, and the current in the wire, $I,$, so this product, $NI,$, in Ampere-turns, is given the name magnetomotive force. For an electromagnet with a single magnetic circuit, of which length $L_\left\{core\right\},$ is in the core material and length $L_\left\{gap\right\},$ is in air gaps, Ampere's Law reduces to:

$NI = H_\left\{core\right\} L_\left\{core\right\} + H_\left\{gap\right\} L_\left\{gap\right\},$

$NI = B\left(frac\left\{L_\left\{core\right\}\right\}\left\{mu\right\} + frac\left\{L_\left\{gap\right\}\right\}\left\{mu_0\right\}\right) qquad qquad qquad qquad \left(1\right) ,$
where $mu = B/H,$

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, $mu_r = mu / mu_0 approx 2000 - 6000,$. So in equation (1) 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.

### Force exerted by magnetic field

When none of the magnetic field bypasses any sections of the core (no flux leakage), the force exerted by an electromagnet on the core material is:

$F = frac\left\{B^2 A\right\}\left\{2 mu_0\right\} qquad qquad qquad qquad qquad qquad \left(2\right) ,$

Where $mu_0 = 4 pi \left(10^\left\{-7\right\}\right),$ Newton Ampere-2. The 1.6 T limit on the field mentioned above sets a limit on the maximum force per unit core area, or pressure, an iron-core electromagnet can exert; roughly:

$frac\left\{F\right\}\left\{A\right\} approx 1000,,kPa = 145,,lbf cdot in^\left\{-2\right\},$

Given a core geometry, the B field needed for a given force can be calculated from (2); if it comes out to much more than 1.6 T, a larger core must be used.

### Closed magnetic circuit

For a closed magnetic circuit (no air gap), such as would be found in an electromagnet lifting a piece of iron, equation (1) becomes:

$B = frac\left\{NImu\right\}\left\{L\right\} qquad qquad qquad qquad qquad qquad \left(3\right) ,$

Substituting into (2), the force is:

$F = frac\left\{mu^2 N^2 I^2 A\right\}\left\{2mu_0 L^2\right\} qquad qquad qquad qquad qquad \left(4\right) ,$

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 part of the magnetic circuit, bringing the magnetic field to the front to form the other pole.

### Force between electromagnets

Force between two electromagnets can be found from

$F = frac\left\{mu_0 m_1 m_2\right\}\left\{4pi r^2\right\}$

Magnetic pole strength of electromagnets can be found from

$m = frac\left\{NIA\right\}\left\{L\right\}$

## High field electromagnets

### Superconducting electromagnets

When a magnetic field higher than the ferromagnetic 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 generate intense magnetic fields. Superconducting magnets are limited by the field strength at which the winding material ceases to be superconducting. Current designs are limited to 10-20 T, with the record of 26.8 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.

### Bitter electromagnets

The highest manmade magnetic fields have been generated by resistive electromagnets of a design invented by Francis Bitter in 1933, called Bitter electromagnets. These consist of a solenoid made of a stack of conducting disks, arranged so that the current moves in a helical path through them. This design has the mechanical strength to withstand the extreme Lorentz forces of the field, which increase with B2. The disks are pierced with holes through which cooling water passes to carry away the heat caused by the high current. The highest continuous field achieved with a resistive magnet is currently (2008) 35 T. The highest continuous magnetic field, 45 T, was achieved with a hybrid device consisting of a Bitter magnet inside a superconducting magnet.

### Exploding electromagnets

The factor limiting the strength of electromagnets is the inability to dissipate the enormous waste heat, so higher fields, up to 90 T, have been obtained from resistive magnets by pulsing them. The highest magnetic fields of all have been created by detonating explosives around a pulsed electromagnet as it is turned on. The implosion compresses the magnetic field to values of around 1000 T for a few microseconds.

## Uses of electromagnets

Electromagnets are widely used in many electric devices, including:

## Definition of terms

$A,$ meters2 cross section area of core
$B,$ Tesla Magnetic field
$F,$ Newton Force exerted by magnetic field
$H,$ Ampere/meter Magnetizing field
$I,$ Ampere Current in the winding wire
$L,$ meter Total length of the magnetic field path $L_\left\{core\right\}+L_\left\{gap\right\},$
$L_\left\{core\right\},$ meter Length of the magnetic field path in the core material
$L_\left\{gap\right\},$ meter Length of the magnetic field path air gap
$m_1, m_2,$ Ampere meter Pole strength of the electromagnets
$mu,$ Newtons/Ampere2 Permeability of the electromagnet core material
$mu_0,$ Newtons/Ampere2 Permeability of free space (or air) = 4π(10-7)
$mu_r,$ - Relative permeability of the electromagnet core material
$N,$ - Number of turns of wire on the electromagnet
$r,$ meters Distance between the two electromagnets

## Patents

• -- Francis Patton's patent of the electromagnet from 1890

## References

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