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Electromagnet

An '''electromagnet''' is a type of magnet in which the magnetic field is produced by the flow of electric Current (electricity)|current. The magnetic field disappears when the current ceases.

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 (tool)|corkscrew) is called a solenoid; a solenoid that is bent into a donut shape so that the ends meet is a Toroidal inductors and transformers|toroid. Much stronger magnetic fields can be produced if a "magnetic core|core" of ferromagnetism|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 become 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 remanence|remanent magnetism, is due to the hysteresis of the material. Applying a decreasing Alternating current|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.

History

Danish scientist Hans Christian Ørsted discovered in 1820 that electric currents create magnetic fields. British scientist William Sturgeon invented the electromagnet in 1823. cited in Windelspecht, Michael. Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 19th Century, xxii, Greenwood Publishing Group, 2003, ISBN 0313319693. His first electromagnet was a horseshoe-shaped piece of iron that was wrapped with about 18 turns of bare copper wire (Electrical insulation|insulated wire didn't exist yet). The iron was varnished to insulate it from the windings. 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 spaced out 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 thousands of turns of wire, including one that could support 2063 pounds. The first major use for electromagnets was in telegraph sounders.

Analysis 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{J}\cdot d\mathbf{A} = \oint \mathbf{H}\cdot d\mathbf{l}

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.

Magnetic circuit - the constant ''B'' field approximation

However, in analyzing a typical DC electromagnet in which the magnetic field path is confined to a single loop or circuit most of which is in core material, the equations can be simplified. The usual assumption made is that the magnetic field strength ''B'' is constant around the magnetic circuit. Most of the magnetic field will be concentrated in the core. Within the core the magnetic field will be approximately uniform across any cross section, so if in addition the core has roughly constant area throughout its length, the field in the core will be constant. This just leaves the air gaps. In the gaps the magnetic field lines are no longer confined by the core, so they 'bulge' out beyond the outlines of the core before curving back to enter the next piece of core material, reducing the field strength in the gap. The bulges are called ''fringing fields''. However, as long as the length of the gap is smaller than the cross section dimensions of the core, the field in the gap will be approximately the same as in the core. In addition, if parts of the core are too near other parts, some of the magnetic field lines will take 'short cuts' and not pass through the entire core circuit. This also occurs in the field near the windings, if the windings are not wrapped tightly around the core. This is called ''leakage flux''. It also results in a lower magnetic field in the core. Therefore the equations in this section are valid for electromagnets for which:
- the magnetic circuit is a single loop.
- the core has roughly the same cross sectional area throughout its length.
- the air gaps are not large compared with the cross sectional dimensions of the core.
- there is negligible leakage flux The main nonlinear feature of ferromagnetic materials is that the B field magnetic saturation|saturates at a certain value, which is around 1.6 T (Tesla_(unit)|Tesla) 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 Paramagnetism|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.

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 (unit)|Ampere-turns, is given the name magnetomotive force. 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:, eq. 36-26
-

NI = H_{core} L_{core} + H_{gap} L_{gap}\,

NI = B(\frac{L_{core}}{\mu} + \frac{L_{gap}}{\mu_0})  \qquad \qquad \qquad \qquad (1)  \,

- :::::::where

\mu = B/H\,

\mu_0 = 4 \pi (10^{-7})\,

Newton Ampere^-2 is the permeability of free space (or air). This is a nonlinear equation, because the Magnetic permeability|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 loop|hysteresis curve. If B is unknown, the equation must be solved by Numerical analysis|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) most core materials saturate at a magnetomotive force of roughly 800 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{B^2 A}{2 \mu_0}   \qquad \qquad \qquad \qquad \qquad \qquad (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{F}{A} \approx 1000\,\,kPa = 145\,\,lbf \cdot in^{-2}\,

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{NI\mu}{L}  \qquad \qquad \qquad \qquad \qquad \qquad (3)  \,

Substituting into (2), the force is:
-

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

It can be seen that to maximize 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

The above methods are inapplicable when most of the magnetic field path is outside the core. For electromagnets (or permanent magnets) with well defined 'poles' where the field lines emerge from the core, the force between two electromagnets can be found using the 'Gilbert model' which assumes the magnetic field is produced by fictitious 'magnetic charges' on the surface of the poles, with pole strength ''m'' and units of Ampere (unit)|Ampere-turn meter. Magnetic pole strength of electromagnets can be found from:

m = \frac{NIA}{L}

The force between two poles is:

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

This model doesn't give the correct magnetic field inside the core, and thus gives incorrect results if the pole of one magnet gets too close to another magnet.

High field electromagnets

Superconducting electromagnets

When a magnetic field higher than the ferromagnetic limit of 1.6 T is needed, Superconducting magnet|superconducting electromagnets can be used. Instead of using ferromagnetic materials, these use Superconductivity|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 ''B''². 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:
- Motors and electrical generator|generators
- Relays, including reed relays originally used in telephone exchanges
- Electric bells
- Loudspeakers
- Magnetic recording and data storage equipment: tape recorders, VCRs, hard disks
- Particle accelerators
- Magnetic locks
- Magnetic separation of materials
- Industrial lifting magnets

Definition of terms

Patents

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

References

External links

- Magnets from Mini to Mighty: Primer on electromagnets and other magnets National High Magnetic Field Laboratory
- Magnetic Fields and Forces Cuyahoga Community College
- Fundamental Relationships School of Geology and Geophysics, University of Oklahoma simple:Electromagnet Category:Types of magnets

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