<p class="MsoNormal"><span style="font-size: 1rem;">Nikola Tesla has been described as the man who
invented the twentieth century because of his understanding of electromagnetism
and the applications he evolved that led to the large-scale generation and
distribution of electricity.</span><br></p><p class="MsoNormal"><span lang="">Now in the twenty-first century, scientists
study the interaction of the magnetic field of the Sun with that of the Earth
using data from the Cluster satellites. Not only does this help us understand
better the physics of our nearest star but it also helps us predict some of the
more damaging effects of large solar flares on the Earth and its near
environment.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1569675468/lsfzwhsttjlsg8iebwz4.jpg" data-filename="lsfzwhsttjlsg8iebwz4" style="width: 325.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:CERN_LHC.jpg" target="_blank"><sup>A section of the LHC. Maximilien Brice, CC BY-SA 4.0</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">In 2008 the Large Hadron Collider (LHC) started
its search for the Higgs Boson and a deeper understanding of the fundamental
nature of matter. The LHC accelerates beams of protons around a synchrotron
ring of 27 km circumference until they reach energies of 7 TeV. To bend protons
around this path requires dipole magnets that produce a magnetic field of 8.4
Tesla (that’s about 100 000 times the magnetic field of the Earth). These
magnets use superconductors and draw currents of about 11 700 amps. They are
143 metres long and 1232 of them are needed. The LHC uses over 2500 other magnets
to guide and collide the proton beams.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">This is just a tiny fraction of the billions
of electromagnetic devices, including motors and drives, and even down to
magnetically controlled nano-rods of gold, nickel and platinum, that require an
understanding of electromagnetism.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">In this article, I will discuss the
inextricable link between moving charges and magnetic fields. When charges move
in a circuit the current is surrounded by a complete loop of magnetic field – a
loop of electric current surrounded by a loop of magnetic field – each linked
with the other. This article will also look at the way current loops create magnetic
fields; the next chapter will take care of how changing magnetic loops can create
currents.<o:p></o:p></span></p><h2><span lang="">FIELDS AROUND CURRENTS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">If we pass an electric current along a wire
and then bring a compass near it, the compass needle (which is a strong magnet)
will be deflected. This is because the current has a magnetic field around it,
as first demonstrated by Hans Christian Oersted in 1820.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">What do we mean by a magnetic field? The compass
needle is deflected because it experiences a force. With a constant current,
the size of the force depends only on how far the needle is from the wire: the
closer it is, the greater the force on the needle – but the needle does not
have to touch the wire. The effect, then, acts at a distance. So we describe
the space around the wire as containing a magnetic field.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1569676206/ozzupyjh1bsoyxcmvear.png" data-filename="ozzupyjh1bsoyxcmvear" style="width: 325.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:VFPt_dipole_magnetic3.svg" target="_blank"><sup>Magnetic dipole. Geek3 - Own work, CC BY-SA 3.0</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">A magnetic field can be represented by ‘field
lines’ that show the shape of the field. We draw the lines close together if we
want to show a strong field, and further apart for a weaker field. The field
has a direction of action. We define the direction of the field at a point as
the direction of the force that would act on an isolated north pole placed there.
(So far no-one has ever found such a thing as an isolated north pole – magnetic
poles always occur in pairs – but it is a useful idea to help define field directions.)
The direction of the magnetic field is from north to south. The Earth has its
own magnetic field, which has been used for hundreds of years in navigation.
Magnetic field is a vector quantity.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1569675937/hh6vj0yapimubkogxeba.png" data-filename="hh6vj0yapimubkogxeba" style="width: 320px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:VFPt_Earths_Magnetic_Field_Confusion.svg" target="_blank"><sup>A sketch of Earth's magnetic field. Geek3 - Own work, CC BY-SA 3.0</sup></a><span lang=""><o:p><br></o:p></span></p><h2><span lang="">MAGNETIC FIELD AND FLUX<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The idea of field lines was one of Faraday’s
important contributions to physics. The patterns we draw around magnets and
coils to describe the shape and variation in strength of fields were first used
by him. He imagined the field lines passing through a surface, and he called this
‘<b>flux’</b><o:p></o:p></span></p><p class="MsoNormal"><span lang="">The flux Φ is defined as:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">flux = field strength
× the area it passes through<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">Φ = BA<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">If the field is not perpendicular to the area,
then the equation becomes<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Φ = BA sin θ<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Flux is measured in <b>webers</b> (Wb).<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The strength of the magnetic field can be
defined in terms of flux and is correctly termed the <b>flux</b> <b>density</b>:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">flux density, B = Φ/A<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">&nbsp;</span></p><p class="MsoNormal"><span lang="">Field lines or flux paths are always in
complete loops. This is not always obvious when we look at fields around
permanent magnets. If we could see the field lines inside the magnet we would
be convinced.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Just as we are used to the idea of electric
circuits being complete paths or loops (we call them ‘circuits), we can use the
idea of magnetic circuits.<o:p></o:p></span></p><h2><span lang="">MAGNETIC CIRCUITS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">In the figure below, the flux is set up by a current flowing through a coil, or
solenoid. The flux, represented by the field lines, is in complete loops. This
is always the case. In some cases, the loops are set up in the space around and
through the coil, while in others, they are contained within a solid core such
as ‘soft iron’. We can think of these complete loops as ‘magnetic circuits’.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">We know from elementary physics that the
physical dimensions of the wire (cross-sectional area and length) in a simple
electric circuit affect the current. Similarly, we shall see here that the
dimensions of a magnetic circuit affect the flux that can be set up.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1569676889/yudivmdyeljwfa8enjtr.png" data-filename="yudivmdyeljwfa8enjtr" style="width: 325.5px;"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Electromagnet_with_air_gap_and_magnetic_circuit_equivalent.png" target="_blank"><sup>Electromagnet with air gap and magnetic circuit equivalent. Frankemann - Own work, CC BY-SA 4.0</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">The flux also depends on the size of the
current and the number of turns on the coil. Without current and turns of the
coil there would be no flux. We say the flux is ‘generated’ by the current
turns. If N is the number of turns, I is the current and Φ is the flux, then:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">NI α Φ<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">To understand how the dimensions of the
magnetic circuit can affect the flux it is probably easier to think about a
transformer. The flux is generated by a primary coil. The iron core has the
interesting and useful property of confining nearly all the flux within the
core. The physical dimensions of the core, its cross-sectional area and the
length all affect the flux.<o:p></o:p></span></p><h2><span lang="">MAGNETIC CIRCUITS COMPARED WITH ELECTRIC CIRCUITS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">At this point it is worth comparing magnetic
circuits with simple electric circuits. A voltage V causes a current I in a
circuit that has electrical resistance. The resistance depends upon the
physical dimensions of the wire and the material of the wire. When A is the
cross-sectional area, l is the length of the wire and ρ is the resistivity of
the material of the wire, then:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">V = IR<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">= I × ρl / A<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">We can write a similar equation for a magnetic
circuit:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">NI = Φ × constant × l /
A<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Just as the current is ‘set up’ by a voltage
in the electric circuit, the flux Φ is set up by the current-turns, NI.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">The constant is 1/μ, where μ is the <b>permeability</b> of the medium within which
the flux is set up. The quantity 1/μA is the magnetic circuit equivalent to
resistance. It is called the <b>reluctance</b>
of the magnetic circuit (R<sub>mag</sub>).<o:p></o:p></span></p><p class="MsoNormal"><span lang="EL">If the magnetic
field is set up in air (which is very similar to a vacuum – free</span> s<span lang="EL">pace – for magnetic fields) then the constant is 1/</span><span lang="">μ<sub>0</sub></span><span lang="EL">, where </span><span lang="">μ<sub>0</sub></span><span lang="EL"> is the</span> p<span lang="EL">ermeability of the
vacuum (free space), with units NA</span><sup>-2</sup><span lang="EL">. In any other</span> m<span lang="EL">edium, the constant is 1/</span><span lang="">μ<sub>0</sub>μ<sub>r </sub></span><span lang="EL">, where </span><span lang="">μ<sub>r</sub></span><span lang="EL">, is the relative permeability of the</span> m<span lang="EL">edium. That is:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">NI = </span><span lang="">Φl / μ<sub>0</sub> μ<sub>r</sub></span>A<o:p></o:p></h4><p class="MsoNormal"><span lang="EL">We think of
permeability as a kind of ‘magnetic conductivity’ – it tells us ho</span>w <span lang="EL">good a medium is at</span> a<span lang="EL">llowing a magnetic field to be established
in that</span> m<span lang="EL">edium. The relative permeability tells us how much
better that medium is</span> c<span lang="EL">ompared to a vacuum.<o:p></o:p></span></p><p class="MsoNormal"><span lang="EL">In electric
circuits, instead of <i>resistance</i> we
often find it more convenient to think</span> o<span lang="EL">f <i>conductance</i>:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">Conductance, G</span> = <span lang="EL">Current</span> / <span lang="EL">potential
difference</span> = σA / l<o:p></o:p></h4><p class="MsoNormal"><span lang="EL">(Remember </span>σ<span lang="EL"> is electrical conductivity, where </span>σ<span lang="EL"> = 1</span><span lang="EL"> </span><span lang="EL">/</span><span lang="EL"> </span><span lang="">ρ</span><span lang="EL">,)</span> w<span lang="EL">e can similarly
define a magnetic conductance, which we call <b>permeance</b></span><b>:</b><o:p></o:p></p><h4 align="center" style="text-align:center"><span lang="EL">permeance, Λ =</span><span lang="EL"> </span><span lang="">Φ / </span><span lang="EL">NI</span> = <span lang="">μ<sub>0</sub> μ<sub>r</sub></span>A / l<o:p></o:p></h4><p class="MsoNormal"><span lang="EL">Magnetic flux
density, or the</span> s<span lang="EL">trength of a magnetic field is</span> m<span lang="EL">easured in tesla (T) in honour of</span><span lang="EL"> </span><span lang="EL">Nikola Tesla
(1856-1943) who was</span> r<span lang="EL">esponsible for many developments</span> i<span lang="EL">n electricity which led to the</span>
w<span lang="EL">idespread use of electricity
as a</span> m<span lang="EL">eans of distributing energy.<o:p></o:p></span></p><h3><span lang="EL">EXAMPLE<o:p></o:p></span></h3><p class="MsoNormal"><span lang="EL">Calculate the
magnetic flux density in a long air-cored</span> s<span lang="EL">olenoid with 2</span>0<span lang="EL"> turns per centimetre and carrying a</span> c<span lang="EL">urrent of 2 A</span>. <span lang="EL">(The permeability of free space</span><span lang="EL"> </span><span lang="">μ<sub>0</sub> = 4π × 10<sup>-7</sup> N A<sup>-2</sup>.)</span><o:p></o:p></p><p class="MsoNormal"><span lang="EL">To solve this
question, use the equation for current-turns:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">NI = </span><span lang="">Φl / μ<sub>0</sub> μ<sub>r</sub></span>A <span lang="EL">= </span><span lang="">Φl / </span>A <span lang="">μ<sub>0</sub> = Bl / μ<sub>0</sub> (since B = Φ /
A)</span><span lang="EL"><o:p></o:p></span></h4><p class="MsoNormal"><span lang="EL">Rearranging:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">B =</span> NI<span lang="">μ<sub>0</sub>
/ l&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (20 turns cm<sup>-1</sup> =
2000 turns m<sup>-1</sup>)</span><o:p></o:p></h4><h4 align="center" style="text-align:center">=
<span lang="EL">2000 </span><span lang="">×</span><span lang="EL"> 2 </span><span lang="">×</span><span lang=""> </span><span lang="">4π × 10<sup>-7</sup></span><span lang="EL"><o:p></o:p></span></h4><h4 align="center" style="text-align:center">=
<span lang="EL">5 </span><span lang="">×</span><span lang="EL"> 10</span><sup>-3</sup> <span lang="EL">T<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="EL">Magnetic flux density in the solenoid</span> = <span lang="EL">5 mT.<o:p></o:p></span></h4><h2><span lang="EL">&nbsp;</span></h2><h2><span lang="EL">FLUX DENSITIES IN SOME USEFUL&nbsp;</span><span lang="EL">MAGNETIC CIRCUITS<o:p></o:p></span></h2><h3><span lang="EL">FLUX DENSITY DUE TO A LONG
SOLENOID<o:p></o:p></span></h3><p class="MsoNormal"><span lang="EL">Imagine a
solenoid of length </span>l <span lang="EL">metres with N turns, forming a circle.
Therefore, when there is a current the flux forms an enclosed loop</span> i<span lang="EL">nside the coil, also of length l. The cross-sectional area of the solenoid,
and</span> s<span lang="EL">o of the tube of flux, is A m<sup>2</sup>. We shall
assume that the medium in the</span> s<span lang="EL">olenoid is air.<o:p></o:p></span></p><p class="MsoNormal">So, let’s <span lang="EL">start with the equation for the flux:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">NI = </span><span lang="">Φl / μ<sub>0</sub></span>A<span lang="EL"><o:p></o:p></span></h4><p class="MsoNormal">Now, since <span lang="">Φ = B × A (flux density × area)</span><span lang="EL">, we can write:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">NI </span>= <span lang="EL">BAl</span><span lang="EL"> </span>/ <span lang="">μ<sub>0</sub>A
= Bl / μ<sub>0</sub></span><o:p></o:p></h4><p class="MsoNormal"><span lang="EL">We can rearrange
this to obtain an equation for the flux density B in</span> a<span lang="EL"> solenoid:<o:p></o:p></span></p><h4 align="center" style="text-align:center">B
= <span lang="">μ<sub>0</sub> NI / l = μ<sub>0</sub> nI</span><o:p></o:p></h4><p class="MsoNormal"><span lang="EL">Where n</span> = <span lang="EL">N/l, the number of turns per metre.</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1569678606/io3zz4uxdbfocjy5ijyg.png" data-filename="io3zz4uxdbfocjy5ijyg" style="width: 325.5px;"><span lang="EL"><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:A_Magnetic_Flux_Loop.png" target="_blank"><sup>Magnetic flux loop. WikiHelper2134 at en.wikipedia, CC BY-SA 3.0</sup></a><span lang="EL"><o:p><br></o:p></span></p><h3><span lang="EL">FLUX DENSITY DUE TO A LONG
STRAIGHT WIRE<o:p></o:p></span></h3><p class="MsoNormal">I<span lang="EL">magine a ring of flux of cross-sectional area A,
around the</span> w<span lang="EL">ire at a distance r from the wire. The wire can be
considercd as part of a</span> v<span lang="EL">ery large single-turn coil, that is, N </span>= <span lang="EL">1. Therefore current:<o:p></o:p></span></p><h4 align="center" style="text-align:center">I
<span lang="EL">= </span><span lang="">Φl / μ<sub>0</sub>A</span><span lang="EL"><o:p></o:p></span></h4><p class="MsoNormal"><span lang="EL">The length l of
the ring of flux is 2</span><span lang="">π</span><span lang="EL">r and, since</span><span lang="EL"> </span><span lang="">Φ =</span><span lang="EL"> BA</span>:<o:p></o:p></p><h4 align="center" style="text-align:center">I
= B<span lang="EL">A</span><span lang="EL"> </span><span lang="EL">2</span><span lang="">π</span><span lang="EL">r</span><span lang="EL"> </span>/ <span lang="">μ<sub>0</sub>A</span><o:p></o:p></h4><p class="MsoNormal"><span lang="EL">Rearranging, we
get:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">B =</span><span lang="EL"> </span><span lang="">μ<sub>0</sub>I / </span><span lang="EL">2</span><span lang="">π</span><span lang="EL">r</span><o:p></o:p></h4><h3><span lang="EL">EXAMPLE<o:p></o:p></span></h3><p class="MsoNormal"><span lang="EL">Calculate the
magnetic flux</span> d<span lang="EL">ensity around a straight wire</span> c<span lang="EL">arrying a current of 10 A at a</span>
d<span lang="EL">istance of </span><b>(</b><b><span lang="EL">a)</span></b><span lang="EL"> 10 cm, </span><b>(</b><b><span lang="EL">b)</span></b><span lang="EL"> 20 cm,</span><span lang="EL"> </span><b>(</b><b><span lang="EL">c)</span></b><span lang="EL"> 100 cm. (The permeability of free</span><span lang="EL"> </span><span lang="EL">space μ0</span> = <span lang="">4π × 10<sup>-7</sup></span><span lang=""> </span><span lang="EL">&nbsp;NA<sup>-2</sup>.)<o:p></o:p></span></p><p class="MsoNormal">To solve this question
<b>(a)</b>, we use the equation for
magnetic flux density:<o:p></o:p></p><h4 align="center" style="text-align:center">B
= <span lang="">μ<sub>0</sub>I / </span><span lang="EL">2</span><span lang="">π</span><span lang="EL">r<o:p></o:p></span></h4><h4 align="center" style="text-align:center">=
<span lang="">4π × 10<sup>-7</sup></span><span lang=""> </span><span lang="">× 5 / 2π × 10 T<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="EL">Magnetic flux density at 10 cm</span><span lang="EL"> </span><span lang="">= 2 × 10<sup>-5</sup> T</span><span lang="EL"><o:p></o:p></span></h4><p class="MsoNormal"><b>(</b><b><span lang="EL">b)</span></b><span lang="EL"> Since r is inversely proportional to</span><span lang="EL"> </span><span lang="EL">B, and since r doubles here, B will</span> h<span lang="EL">alve to 1 </span><span lang="">×</span><span lang="EL"> 10<sup>-5</sup> T</span>.<o:p></o:p></p><p class="MsoNormal"><b>(</b><b><span lang="EL">c)</span></b><span lang="EL"> With a value for r of 100 cm, the</span><span lang="EL"> </span><span lang="EL">field strength is 2 </span><span lang="">×</span><span lang="EL"> 10<sup>-6</sup> T<o:p></o:p></span></p><h2><span lang="EL">THE EFFECT OF IRON<o:p></o:p></span></h2><p class="MsoNormal"><span lang="EL">Iron has a very
large relative permeability, which is why it is useful for ma</span>k<span lang="EL">in</span>g e<span lang="EL">lectromagn</span>e<span lang="EL">ts, for example. When
a coil is wound on a soft iron core, the</span> m<span lang="EL">agn</span>e<span lang="EL">tic fi</span>e<span lang="EL">ld produced is about a thousand times stronger
than it would be</span> i<span lang="EL">f the iron were not there. Iron also has
the property of losing most of the</span>
m<span lang="EL">agn</span>e<span lang="EL">tism as soon as the current stops flowing. This is why it is des</span>c<span lang="EL">ribed</span><span lang="EL"> </span><span lang="EL">‘soft’. A magnetically ‘hard’ metal such
as steel would retain much of the</span>
m<span lang="EL">agnetism if it were used in
the same coil. The magnetic flux density in a</span> s<span lang="EL">olenoid with an iron
core is:<o:p></o:p></span></p><h4 align="center" style="text-align:center">B
= μ<sub>r</sub>μ<sub>0</sub> NI / l<o:p></o:p></h4><p class="MsoNormal"><span lang="EL">Where N number of
turns and l = length of flux loop. The value of</span><span lang="EL"> </span>μ<sub>r</sub><span lang="EL"> for</span> i<span lang="EL">ron is about 1000.<o:p></o:p></span></p><p class="MsoNormal"><span lang="EL">We can say that
iron is a ‘good conductor</span>’<span lang="EL"> of magnetism. Many other magnetic</span> m<span lang="EL">aterials have high relative permeabilities but are less dense than iron.
These find</span> u<span lang="EL">ses where light weight is an advantage, such as in
miniature earphones and the</span><span lang="EL">
</span><span lang="EL">small motors used inside CD
and DVD drives.<o:p></o:p></span></p><h2><span lang="EL">MAGNETIC CIRCUITS AND SOME</span><span lang="EL"> </span><span lang="EL">ELECTROMAGNETIC DEVICES<o:p></o:p></span></h2><p class="MsoNormal"><span lang="EL">Many simple
electromagnetic devices can be understood by</span> u<span lang="EL">sing the idea of
magnetic circuits. One is the</span><span lang="EL"> </span><b>e</b><b><span lang="EL">lectromagnetic</span></b><span lang="EL"> <b>relay</b>,
which allows remote switching of</span> s<span lang="EL">everal circuits at once. If we examine the
flux path in a relay</span>, w<span lang="EL">e see that there is a ‘high reluctance’
air gap between the</span> c<span lang="EL">ore of the electromagnet and the armature. The</span> f<span lang="EL">lux in this magnetic circuit is weak. When the electromagne</span>t i<span lang="EL">s ‘energized’ by a current in it, the armature is attracted</span> t<span lang="EL">owards the electromagnet core. This reduces the reluctance of</span> t<span lang="EL">he magnetic circuit and a strong flux is established. It should</span> a<span lang="EL">lso be noted that the force between the core and the</span> a<span lang="EL">rmature is in a straight line and that the armature moves in</span> t<span lang="EL">he same direction.<o:p></o:p></span></p><p class="MsoNormal"><span lang="EL">Many simple
motors also produce rotation when the <i>rotor</i></span> m<span lang="EL">oves to make a magnetic circuit with a lower reluctance. They</span> a<span lang="EL">re called <b>reluctance</b> <b>motors</b> and are used in disk drives and</span> f<span lang="EL">ans in computers. The <i>stepper motor</i>
found in all computer</span> p<span lang="EL">rinters is also a more sophisticated
relative of the</span> r<span lang="EL">eluctance motor.<o:p></o:p></span></p><p class="MsoNormal"><b><span lang="EL">The figure below shows a simple reluctance motor</span></b><span lang="EL">. The rotor can be a</span> p<span lang="EL">ermanent magnet or an</span> e<span lang="EL">lectromagnet (or even a soft iron bar</span>). <o:p></o:p></p><p class="MsoNormal"><span lang="EL">When the coils
are energized so that one pole becomes a north</span> p<span lang="EL">ole and the other a
south pole, the rotor experiences a sideways</span><span lang="EL"> </span><i>a</i><i><span lang="EL">lignment</span></i><span lang="EL"> force. In trying to line up, the rotor is
reducing the ‘high</span> r<span lang="EL">eluctance</span>’<span lang="EL"> gap in a magnetic
circuit so that a stronger flux path</span>
c<span lang="EL">an be established. The coils
could be connected to an a.c. source. As the rotor turns it is in turn
attracted to and repelled</span> f<span lang="EL">rom the changing poles, continually trying
to produce the lowest</span> r<span lang="EL">eluctance path for the flux. (The
rotational speed of this motor</span> w<span lang="EL">ill depend on the frequency of the a.c.
supply. These are often</span> a<span lang="EL">lso called <i>synchronous</i> motors.)</span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1569677229/yuaht1bnitdliwimvj83.jpg" data-filename="yuaht1bnitdliwimvj83" style="width: 325.5px;"><span lang="EL"><br></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Switched-reluctance-motor-characteristics-work-principles-t.jpg" target="_blank"><sup>The reluctance motor. Hamidreza D - Own work, CC BY-SA 4.0</sup></a><span lang="EL"><br></span><o:p></o:p></p><h2><span lang="EL">FORCES ON WIRES CARRYING
CURRENTS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="EL">In a wire carrying a current and placed at right
angles to a</span> m<span lang="EL">agnetic field. We can predict the direction of the</span> f<span lang="EL">orce on the wire by using Fleming’s left-hand rule. The wire will tend to</span> m<span lang="EL">ove in the direction of the force. This link between a wire carrying a
current</span> a<span lang="EL">nd its movement in a magnetic field is used in the
moving coil electric</span> m<span lang="EL">otor.<o:p></o:p></span></p><p class="MsoNormal"><span lang="EL">The size of the
force F depends upon the current <i>I</i> in
the wire of length </span><i>l </i><span lang="EL">in the</span> m<span lang="EL">agnetic field of strength B. That is:<o:p></o:p></span></p><ul><li>F <span lang="">α I</span><span lang="EL">, the
current in the wire</span></li><li>F <span lang="" style="font-size: 1rem;">α l</span><span lang="EL" style="font-size: 1rem;">, the length of wire in the field</span></li><li>F <span lang="" style="font-size: 1rem;">α</span><span lang="EL" style="font-size: 1rem;"> B, the magnetic flux density</span></li></ul><p class="MsoNormal"><span lang="EL">Taken together,
these can be expressed as:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">F </span>= <span lang="EL">kIlB<o:p></o:p></span></h4><p class="MsoNormal"><span lang="EL">where <i>k</i> is a constant.<o:p></o:p></span></p><p class="MsoNormal"><span lang="EL">We choose the
units of B to make k</span> =<span lang="EL"> 1, as follows. Suppose the magnetic</span> f<span lang="EL">ield is such that a wire 1 metre long carrying a current of 1 ampere feels
a</span> f<span lang="EL">orce of 1 newton. We shall define the flux density
B as 1 newton per ampere</span> m<span lang="EL">etre (N A</span><sup>-</sup><sup><span lang="EL">1</span></sup><span lang="EL"> m</span><sup>-1</sup><span lang="EL">). Therefore we have:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">1 N </span>= <span lang="EL">k </span><span lang="">×</span><span lang="EL"> (N A<sup>-1</sup> m<sup>-1</sup>) </span><span lang="">×</span><span lang="EL"> 1 A </span><span lang="">×</span><span lang=""> </span><span lang="EL">1 m<o:p></o:p></span></h4><p class="MsoNormal"><span lang="EL">The newton per
ampere metre is called a <b>tesla</b>,
symbol T. Small magnetic</span> f<span lang="EL">ields are measured in </span>μ<span lang="EL">T (micro-tesla). The magnitude of the Earth’s magnetic</span> f<span lang="EL">ield varies between 24 </span>μ<span lang="EL">T and 66 </span>μ<span lang="EL">T. In the UK it is
about 49 </span>μ<span lang="EL">T</span>. <span lang="EL">Under these conditions k </span>= <span lang="EL">1. So we have:</span><o:p></o:p></p><h4 align="center" style="text-align:center"><b><span lang="EL">F</span></b><b><span lang="EL"> </span></b><b><span lang="EL">= IlB<o:p></o:p></span></b></h4><p class="MsoNormal"><span lang="EL">By writing the
equation for the force like this we are being consistent with</span> o<span lang="EL">ther ‘forces in fields’:<o:p></o:p></span></p><ul><li><span lang="EL">In a uniform electric field, force </span>= <span lang="EL">charge </span><span lang="">×</span><span lang=""> </span><span lang="EL">electric field strength
(F = q </span><span lang="">×</span><span lang="EL"> E)</span></li><li>In a gravitational field, force <span style="font-size: 1rem;">= </span><span lang="EL" style="font-size: 1rem;">mass </span><span lang="" style="font-size: 1rem;">× </span><span lang="EL" style="font-size: 1rem;">gravitational field strength (F = m </span><span lang="" style="font-size: 1rem;">×</span><span lang="EL" style="font-size: 1rem;"> g)</span></li></ul><p class="MsoNormal"><span lang="EL">The general idea
being:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">Force </span>= <span lang="EL">magnitude of quantity feeling the force </span><span lang="">×</span><span lang="EL"> field strength<o:p></o:p></span></h4><p class="MsoNormal"><span lang="EL">The ‘thing’
feeling the force in a magnetic field is a current-carrying wire (Il). So:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="EL">Magnetic force </span>= <span lang="EL">Il </span><span lang="">×</span><span lang="EL"> B<o:p></o:p></span></h4><p class="MsoNormal"><span lang="EL">The force on a
coil of N turns would be N times greater than on a single wire,</span> n<span lang="EL">amely N </span><span lang="">×</span><span lang="EL"> IlB</span>.<o:p></o:p></p><p class="MsoNormal"><span lang="EL">Force F is a
maximum when the field and current are perpendicular (with</span> m<span lang="EL">agnetic field constant). If the angle is smaller, the force is reduced</span>.<o:p></o:p></p><h4 align="center" style="text-align:center"><span lang="EL">F = Il </span><span lang="">×</span><span lang="EL"> B sin θ<o:p></o:p></span></h4><p class="MsoNormal">A special apparatus
for measuring the magnetic flux density is known as the current balance.<span lang="EL"><o:p></o:p></span></p><h3><span lang="EL">EXAMPLE<o:p></o:p></span></h3><p class="MsoNormal"><span lang="EL">Calculate the
flux density of the</span> m<span lang="EL">agnetic field that will apply a force</span> o<span lang="EL">f 0.1 N per metre to a wire</span> c<span lang="EL">arrying a current of 7 A</span>.<o:p></o:p></p><h4 align="center" style="text-align:center">Solution:
Since F = IlB or B = F / Il, then B = 0.1 N / 7 A <span lang="">× 1 m =
0.0143 N (Am)<sup>‑1</sup></span><o:p></o:p></h4><h4 align="center" style="text-align:center">Flux
density = 14.3 mT<o:p></o:p></h4><p class="MsoNormal"><span lang="EL">&nbsp;</span></p><p class="MsoNormal">I guess I should be
stopping here for now. But, in my next article, I will continue by discussing
on how the unit of electric current, the ampere was being determined and also
on forces on charged particles in beams with some other interesting aspects of
electromagnetism.<o:p></o:p></p><p class="MsoNormal">Till then, I remain my
humble self, @emperorhassy.<o:p></o:p></p><p>

















































































































































































































































</p><h2>Thanks for reading.</h2><h2>REFERENCES</h2><p><a href="https://en.wikipedia.org/wiki/Electromagnetism" target="_blank">https://en.wikipedia.org/wiki/Electromagnetism</a><br></p><p><a href="https://phys.org/news/2017-10-electromagnetism-everyday-life.html" target="_blank">https://phys.org/news/2017-10-electromagnetism-everyday-life.html</a><br></p><p><a href="https://en.wikipedia.org/wiki/Magnetic_flux" target="_blank">https://en.wikipedia.org/wiki/Magnetic_flux</a><br></p><p><a href="https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux" target="_blank">https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/a/what-is-magnetic-flux</a><br></p><p><a href="https://circuitglobe.com/what-is-a-magnetic-circuit.html" target="_blank">https://circuitglobe.com/what-is-a-magnetic-circuit.html</a><br></p><p><a href="https://www.sciencedirect.com/topics/engineering/magnetic-circuits" target="_blank">https://www.sciencedirect.com/topics/engineering/magnetic-circuits</a><br></p><p><a href="https://en.wikipedia.org/wiki/Magnetic_circuit" target="_blank">https://en.wikipedia.org/wiki/Magnetic_circuit</a><br></p><p><a href="https://dipslab.com/difference-between-electrical-circuit-and-magnetic-circuit/" target="_blank">https://dipslab.com/difference-between-electrical-circuit-and-magnetic-circuit/</a><br></p><p><a href="https://circuitglobe.com/difference-between-magnetic-and-electric-circuit.html" target="_blank">https://circuitglobe.com/difference-between-magnetic-and-electric-circuit.html</a><br></p><p><a href="https://www.saburchill.com/physics/chapters/0050.html" target="_blank" style="background-color: rgb(255, 255, 255); font-size: 1rem;">https://www.saburchill.com/physics/chapters/0050.html</a><br></p><p><a href="https://www.allaboutcircuits.com/video-lectures/magnetism-and-electromagnetism/" target="_blank">https://www.allaboutcircuits.com/video-lectures/magnetism-and-electromagnetism/</a><br></p><p><a href="https://www.britannica.com/science/magnetic-circuit" target="_blank">https://www.britannica.com/science/magnetic-circuit</a><br></p><p><a href="https://www.electronics-tutorials.ws/electromagnetism/magnetism.html" target="_blank">https://www.electronics-tutorials.ws/electromagnetism/magnetism.html</a><br></p><p><a href="https://science.howstuffworks.com/electromagnet.htm" target="_blank">https://science.howstuffworks.com/electromagnet.htm</a><br></p><p><a href="https://www.eolss.net/Sample-Chapters/C05/E6-39A-01-02.pdf" target="_blank">https://www.eolss.net/Sample-Chapters/C05/E6-39A-01-02.pdf</a><br></p><p><a href="https://study.com/academy/lesson/understanding-forces-on-current-carrying-wires-in-magnetic-fields.html" target="_blank">https://study.com/academy/lesson/understanding-forces-on-current-carrying-wires-in-magnetic-fields.html</a><br></p><p><a href="https://courses.lumenlearning.com/physics/chapter/22-10-magnetic-force-between-two-parallel-conductors/" target="_blank">https://courses.lumenlearning.com/physics/chapter/22-10-magnetic-force-between-two-parallel-conductors/</a><br></p><p><a href="http://physicstasks.eu/2112/magnetic-force-between-two-wires-carrying-current" target="_blank">http://physicstasks.eu/2112/magnetic-force-between-two-wires-carrying-current</a><br></p><p><br></p><p class="MsoNormal"><o:p></o:p></p>