During the 1820s Faraday sought to discover how to make electricity from magnetism. He achieved success with the device pictured above on 29 August 1831.

When he passed an electric current through one coil he induced an electric current in the other coil, which flowed for a very brief period of time.

When Michael Faraday made his discovery of electromagnetic induction in 1831, he hypothesized that a changing magnetic field is necessary to induce a current in a nearby circuit. To test his

hypothesis he made a coil by wrapping a paper cylinder with wire. He connected the coil to a galvanometer, and then moved a magnet back and forth inside the cylinder.

During the 1820s Faraday sought to discover how to make electricity from magnetism. He achieved success with the device pictured above on 29 August 1831. It's made from everyday materials such as wire made for bonnets, although the iron ring seems to have been specially made. Making the induction ring was a tedious process since Faraday had to wind the coils of wire on opposite sides of the ring and insulate them with cotton. It probably took him ten days to make it. When he passed an electric current through one coil he induced an electric current in the other coil, which flowed for a very brief period of time.

Faraday’s magnetic induction experiment.

Ampere's law applied to an infinitely-long wire predicts a magnetic field of strength B=0I/(2r) a

radial distance r from the wire.  The field B is tangential to a circle of radius r centered on the

wire.

                                                          

We therefore have (B/I)=(0/2)(1/r).  B/I is

proportional to 1/r, and when plotted versus 1/r will yield a straight line with slope (0/2).

                                                                                 

                                                         

Consider the magnetic field around an infinitely long wire due to a current I flowing through the wire.

                                              

    

                                                                               

But B has the same value a distance a away from

the rod, hence                                                        

For the simple example, only one current linking the closed path C, therefore N = 1

Electromagnetic Basics

1,2,3,4In this section we will look at the general electromagnetic principles which are widely employed in engineering. This is a very short introduction to a complex subject. You should find yourself a good book on magnetism and electromagnetism if you want to develop a better understanding in this area. You can also find most of these concepts examined in detail at Fizzics Fizzle.Electromagnetic Fields and ForcesBefore we look specifically at the case of the coilgun it will be beneficial to briefly examine the fundamentals of electromagnetic fields and forces. Whenever there is charge in motion there is a corresponding magnetic field associated with it. This motion can take the form of current in a wire, orbital electrons in a molecule or the flow of a plasma etc. To help us with our understanding of electromagnetics we employ the concepts of the electromagnetic field and magnetic poles. The differential vector equations which describe this field were developed by James Clark Maxwell.

 1. Systems of Units -Just to make life difficult, there are three systems of units in popular use, namely the Sommerfield, Kennely and Gaussian systems. Since each system has different units for many of the quantities things can become confusing. I'll be using the Sommerfield System as outlined below:

QuantityUnitHAm-1weber (W)Btesla (T)Magnetisation MAm-1Intensity of Magnetisation

I-m

Am2

Table 1. Sommerf

ield System of Units

 2. Biot-Savart Law -It is

possible to

determine the

magnetic field

generated by a current element

using the Biot-Savart Law.

                                                                                                   

  Fig 2.1

 

Eqn 2.1

 where    H is the field component at a distance r generated by the current i flowing in the elemental length    l . u is a unit vector directed radially from    l.We can determine the magnetic field generated by some basic current configurations using this law. Consider an infinitely long wire carrying a current i. We can use the Biot-Savart Law to derive a general solution for the field at any distance from the wire. I won't repeat the derivation here, any book on electromagnetism will detail this. The general solution is: 

Eqn 2.2

  

                                                                                     Fig 2.2

 The field is circular and concentric with the current. Another configuration which has an analytical solution is the axial field of a current loop. While we can develop an analytical solution for the axial field, it's not possible to do this for the field in general. In order to find the field at some arbitrary point we need to solve complex integral equations, this best done with numerical techniques.. 3. Ampere's Law -This is an alternative method of determining the magnetic field due to a group of current carrying conductors. The law can be stated as: 

Eqn 3.1

 where N is the number of conductors carrying a current i and l is a line vector. The integration must form a closed line around the current. Looking at the infinite wire again we can apply Ampere's Law as follows:

 

                                          Fig 3.1

 We know that the field is circular and concentric with the current so H can be integrated around the current at a distance r to give: 

   Eqn 3.2

 The integration is very straightforward and shows how Ampere's Law can be applied to provide quick solutions in some types of geometry. A knowledge of the field pattern necessary before this Law can be applied.

 4. Field of a SolenoidWhen charge flows in a coil, it generates a magnetic field whose direction is given by the right hand convention - Take your right hand and curl your fingers in the direction of the current while extending your thumb, the direction of your thumb now points to the magnetic north end of the coil. The convention for the direction of flux has the flux emerging from a north pole and terminating on a south pole. The field and flux lines form closed loops around the coil. Remember that these lines don't actually exist as such, they simply connect points of equal value. It's a bit like the contours on a map where the lines represent points of equal height. The ground height varies continuously between these contours, in the same way the field and flux from a coil are continuous (the continuum isn't necessarily smooth - a disctete change in permeability will cause field values to change sharply, a bit like a cliff face in the map analogy).

 

                                                                                        Fig 4.1

 If the solenoid is long and thin then the field inside the solenoid can be considered almost uniform. 5. Ferromagnetic MaterialsProbably the most well known ferromagnetic material is iron but there are other elements such as cobalt and nickel, as well as numerous alloys like silicon steel. Each material has a particular property which makes it suitable for its application. So what do we mean by a ferromagnetic material? Put simply, a ferromagnetic material is attracted by a magnet. While this is correct it's hardly a useful definition and it doesn't tell us why the attraction occurs. The detailed theory of the magnetism of materials is quite a complex subject involving quantum mechanics so we'll stick to a simpler conceptual description. As you know, the flow of charge generates a magnetic field so whenever we find charge in motion we should expect an associated field. In a ferromagnetic material the orbiting electrons are arranged in such a way as to generate a small magnetic field. Now this means that the material is effectively composed of many tiny current loops which have their own magnetic field. Normally the atoms are orientated in small groups called domains, these are directed randomly throughout the material so there is no net magnetic field. However if we apply an external field to the ferromagnetic material from a coil or permanent magnet, the current loops try and align with this field - the domians which are most aligned with the field 'grow' at the expense of the less well aligned domians. When this occurs it results in a net magnetisation and attraction between the material and the magnet/coil. 6. Magnetic Induction and Permeability -The production of a magnetic field has an associated magnetic flux density, also known as magnetic induction. The induction B is linked to the field by the permeability of the medium through which the field penetrates. 

Eqn 6.1

 where    0 is the permeability of free space and    r is the relative permeability. The unit of induction is the tesla. 7. Magnetisation -The magnetisation of a material is a measure of it's magnetic 'strength'. Magnetisation can be inherent in the material, such as in a permanent magnet or it can be generated by external fields sources such as a solenoid. The magnetic induction in a material can be expressed as the vector sum of the magnetisation, M, and the magnetic field, H. 

Eqn 7.1

 8. Magnetomotive Force (mmf)-This is analogous to electromotive force (emf) and is used in magnetic circuits to determine the flux densities in the various circuit paths. Mmf is measured in ampere-turns or just amperes. The magnetic circuit equivalent of resistance is reluctance which is defined as

 

Eqn 8.1

 where l is the length of the circuit path,     is the permeability, and A is the cross-sectional area.Let's look at a simple magnetic circuit: 

                                                                               Fig 8.1

 The torus has a mean radius of r and a cross-sectional area A. The mmf is supplied from a coil with N turns carrying a current i. The calculation of reluctance is complicated by the nonlinearity of the materials permeability. 

 

Eqn 8.2

 If the reluctance can be determined then we can calculate the flux which exists in the magnetic circuit.

 

Index

Maxwell's equations concepts

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Maxwell's Equations

Faraday's Law of InductionThe line integral of the electric field around a closed loop is equal to the negative of the rate of change of the magnetic flux through the area enclosed by the loop. This line integral is equal to the generated voltage or emf in the loop, so Faraday's law is the basis for electric generators. It also forms the basis for inductors and transformers. Application to voltage generation in a coil

Gauss' law, electricity Gauss' law, magnetism Faraday's law Ampere's lawMaxwell's EquationsIndex

Maxwell's equations concepts HyperPhysics***** Electricity and Magnetism R NaveGo Back

Ampere's LawIn the case of static electric field, the line integral of the magnetic field around a closed loop is proportional to the electric current flowing through the loop. This is useful for the calculation of magnetic field for simple geometries.

Gauss' law, electricity Gauss' law, magnetism Faraday's law Ampere's lawApply to charge conservationMaxwell's Equations

Figure 6: Current i charging a capacitor as an illustration of Maxwell’s displacement current (see text).