# 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 electrician William Sturgeon invented the electromagnet in 1900. The first electromagnet was a horseshoe-shaped piece of iron that was wrapped with a loosely wound coil consisting of several turns of wire. When a current was passed through the coil, the iron became magnetized and when the current was stopped, the coil was de-magnetized. Sturgeon displayed its power by lifting nine pounds with a seven-ounce piece of iron wrapped with wires through which the current of a single-cell battery was sent.

## 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 increase the effective current available to generate magnetic field, the wire is commonly configured as a coil, where many segments of wire sit side by side. A coil forming the shape of a straight tube (similar to a corkscrew) is called a solenoid; a solenoid that is bent so that the ends meet is a toroid. Much stronger magnetic fields can be produced if a "core" of paramagnetic or 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. File:Electromagnetism.svg Magnetic fields caused by coils of wire follow a form of the right-hand rule (for conventional current or left hand rule for electron current) [1]. If the fingers of the left hand are curled in the direction of electron current flow through the coil, 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.

## Force on ferromagnetic materials

Computing the force on ferromagnetic materials is, in general, quite complex. This is due to fringing field lines and complex geometries. It can be simulated using finite element analysis. However, it is possible to estimate the maximum force under specific conditions. If the magnetic field is confined within a high permeability material, such as certain steel alloys, the maximum force is given by:

${\displaystyle F={\frac {B^{2}A}{2\mu _{o}}}}$

Where:

• F is the force in newtons
• B is the magnetic field in teslas
• A is the area of the pole faces in square meters
• ${\displaystyle \mu _{o}}$ is the permeability of free space

See energy in a magnetic field for more details on the derivation.

In the case of free space (air), ${\displaystyle \mu _{o}=4\pi \cdot 10^{-7}\,{\mbox{H}}\cdot {\mbox{m}}^{-1}}$, the force per unit area (pressure) is:

${\displaystyle P\approx 398\,\mathrm {kPa} }$ or ${\displaystyle 57.7\,{\mbox{lbf}}\cdot {\mbox{in}}^{-2}}$ @ B = 1 tesla

${\displaystyle P\approx 1592\,\mathrm {kPa} }$ or ${\displaystyle 230.8\,{\mbox{lbf}}\cdot {\mbox{in}}^{-2}}$ @ B = 2 teslas

In a closed magnetic circuit:

${\displaystyle B={\frac {\mu NI}{L}}}$

Where:

• N is the number of turns of wire around the electromagnet
• I is the current in amperes
• L is the length of the magnetic circuit
• ${\displaystyle \mu =\mu _{o}\mu _{r}}$ is the permeability of the magnetic core
• ${\displaystyle \mu _{r}}$ is the relative permeability of the electromagnets core

Substituting above,

${\displaystyle F={\frac {\mu ^{2}N^{2}I^{2}A}{2\mu _{0}L^{2}}}.}$

In order to build a strong electromagnet, a short magnetic circuit with large area is preferred. Most ferromagnetic materials saturate around 1 to 2 teslas. This occurs at a field intensity of:

${\displaystyle H\approx 787\ {\mbox{ampere.turns/meter or}}\ 20\ {\mbox{ampere.turns/inch}}.}$

For this reason, there is no reason to build an electromagnet with a higher field intensity. Industrial lifting electromagnets are designed with both pole faces at one side (the bottom). This confines the field lines to maximize the magnetic field. It's like a cylinder within a cylinder. Many loudspeaker magnets use a similar geometry, although the field lines are radial from the inner cylinder rather than perpendicular to the face.

## Force between Electromagnets

Force between two electromagnets can be found from

          F = μ0*m1*m2/(4*π*r2)


where μ0=Permeability of free space =4π.10-7

m1,m2 = pole strength of electromagnets 1 and 2 resp.

r = distance between electromagnets

Magnetic pole strength of electromagnets can be found from

          m = N.i.A/L

              where N = no of turns in electromagnet coil.
i = Current through electromagnet coil
A = cross sectional area of electromagnet ( in flux path direction)
L = length of electromagnet


## Use of electromagnets

Electromagnets are widely used in many applications, including: