### Beginning of the end?

I just discovered I didn't do that much revision. I don't even dare to estimate how long I've spent. Everything in the notes seems so unfamiliar. I know some of the stuff but I can't do questions. And exams are consist of questions. Exam stress takes all the concentration out. Leaving me sitting somewhere doing a lot of daydreaming and wondering around. The volume needed to done is expanding all the time, thus underestimation is unavoidable. The stake of the exam is high. Not just the progession to 4th year, but my not-too-much-left reputation as well. I have no idea how I am going to survive the exam. May be this is the beginning of the end? I rather have the end of the beginning, which means that the exams would be a milestone of my so-called career. But there are so many ends. So exams must be an end of some sort. I don't know, that's nothing to do with exam materials and it would be quite time-consuming to proof...

## 10 comments by 1 or more people

[Skip to the latest comment]## Sue

Try not to worry so much, academic qualifications aren’t everything, you only have to look at the person who won The Apprentice to realise that. There’s no point getting all worked up about it anyway. Here’s a poem to cheer you up:-

Stoned and lonely in the union bar

looking for a warm student

to fall upon. Someone gentle

and undemanding. History perhaps?

Not Maths or English.

Not English. I’m in

no mood to be laid

alongside our literary heritage

allocated my place in her

golden treasury of flesh.

Geography might do the job.

To snuggle up to

shifting continents and

ocean currents. Swap tonnage

and compare monsoons.

Even Chemistry. Someone

tangible. Flasks, bubblings

and a low flame underneath.

With someone warm like this

I’d take my chances.

Maths would find in me no questions

English Lit. no answers.

15 Jun 2008, 00:01

## Tom Duncan

Electromagnetic Induction

Inducing e.m.f.s

An electric current creates a magnetic field the reverse effect of producing electricity by magnetism was discovered independently in 1831 by Faraday in England and Henry in America and is called electromagnetic induction. Induced e.m.f.s. can be generated in two ways.

a) By relative movement (the generator effect). If a bar magnet is moved in and out of a stationary coil of wire connected to a centre-zero galvanometer a small current is recorded during the motion but not at other times. Movement of the coil towards or away from the stationary magnet has the same results. Relative motion between magnet and coil is necessary.

Observation shows that the direction of the induced current depends on the direction of relative motion. Also the magnitude of the current increases with the speed of motion, the number of turns on the coil and the strength of the magnet.

Although it is current we detect in this demonstration, an e.m.f. is the more basic quantity and is always present even when the coil is not in a complete circuit. The value of the induced current depends on the resistance of the circuit as well as on the induced e.m.f.

We will be concerned here only with e.m.f’s induced in conductors but they can be produced in any medium – even a vacuum, where they play a basic role in the electromagnetic theory of radiation.

b) By changing a magnetic field (the transformer effect). In this case two coils are arranged one inside the other. One coil, called the primary, is in series with a 6V d.c. supply, a tapping key and a rheostat. The other, called the secondary, is connected to a galvanometer. Switchibg the current on or off in the primary causes a pulse of e.m.f. and current to be induced in the secondary. varying the primary current by quickly altering the value of the rheostat has the same effect. Electromagnetic induction thus occurs when ther is any change in the primary current and so also in the magnetic field it produces.

Cases of electromagnetic induction in which current changes in one circuit causes induced e.m.f’s in a neighbouring circuit, not connected to the first, are examples of mutual induction – the transformer principle.

The induced e.m.f. is increased by having a soft iron rod in the coils or, better still, by using coils wound on a complete iron ring. It is worth noting that the secondary current is in one direction when the primary current increases and in the opposite direction when it decreases.

This comes from an A level physics book so it might not be very helpful but sometimes it’s good to remember the basics. If you’ve found any of this useful I can find you some more advanced information tomorrow. The other thing is that I can’t type the equations, I’m not sure if there’s a way of doing that.

15 Jun 2008, 01:21

Thanks for all the support and comments. I am actually sort of alright. I am quite prepared for the outcomes of exam (not the exams themselves). Just the exam stress. Don’t worry me too much. I am not going to kill myself. I may not be as bad as I thought, sorry to sound terrible in the entry. I think I would be better off burying my nose in my notes rather than wondering around on internet.

15 Jun 2008, 11:50

## Christopher C. Davis

I wasn’t trying to worry you.

Storage and Transport of Energy by Electro magnetic FieldsThe total energy (per unit volume) stored by a system of elctric and magnetic fields is, + in an isotropic medium,

p = 1/2 (D. E + B . H) = 1/2 (EEoE2 + uuoH2).

In an electromagnetic wave this energy is transported along in the direction of energy flow, which in an isotropic medium is in the same direction as the wave vector (the normal to the wavefront). The rate of energy flow across unit areaper second is given by a vector S called the Poynting vector. If we consider a plane-polarized wave with fields Ex and Hy, then S is in the direction of the z axis and has magnitude

In general

S = E x H.

(there’s a whole page of equations to explain this along with a diagram which is actually quite pretty)

The Reflection and Refraction of a Plane Electromagnetic Wave at the Boundary Between Two Isotropic Media of Different Refractive Index.The diagram shows the directions of propagation and field directions for the incident, reflected, and transmitted elctromagnetic waves at a planar boundary. The discussion is restricted to P-waves, but a similar discussion is readily developed for S-waves. For the incident wave the electric field varies with position as fo S-waves. For the incident wave the electric field varies with position.

The Vector Differential Equation for Light Rays

Proof that(d/ds) (nd*r*/ds) =gradnThe optical length L in a uniform homogenous medium is nl, where n is the (constant) refractive index along a straight line of geometric path length l . In a situation where the refractive index varies from point to point the optical path from point P1 to point P2 is

L = elongated s (P2 at the top and P1 at the bottom) n (

r)ds,where s is measured along the path of the ray. Fermats’s principle states that the actual path taken by a ray will be the one for which L is a minimum.

We can generalize the idea of the optical length by introducing a quatity called the optical path or eikonal.

Stored Electromagnetic Energy in Anisotropic MediaIf we wish the stored energy density in an electromagnetic field to be the same in an anisotropic medium as it is in an isotropic one then we require

U = 1/2(E.D + B.H)

Where we have assumed that the medium is nonconductive so that

j= 0 gives the rate of change of stored energy within unit volume, which must also be given by the time derivative.exxExEx + exyEyEx + exzEzEx + eyxExEy + eyyEyEy

+eyzEzEy + ezxExEz +ezyEyEz +ezzEzEz

=exxExEx + ExyEyEx + exzEzEx + eyxExEy

+eyyEyEy + eyzEzEy +ezxExEz +ezyEyEz + ezzEzEz

Clearly exy = eyz = ezx; etc. so the dielectric tensor only has six independent terms. By working in the principal cocordinate system, all the off-diagonal terms of the dielectric tensor become zero, which graetly simplifies consideration of the wave propagation characteristics of anisotropic crystals. In this case we can write

Dx = eoexEx; Dy = eoeyEy; Dz = eoezEz,

where we are writing ex = exx, etc., for simplicity and the elctrical energy density in the crystal becomes

UE = 1/2*E.D* = 1/2eo (D2x/ex = D2y/ey = D2z/ez)

This shows that the electric displacement vectors from a given point that correspond to a constant stored electrical enery describe an ellipsoid.

I might come back with some more. It depends how much you want to go into anisotropics really.

15 Jun 2008, 13:01

## Walter Wilkinson

~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-150 o Resistivity at 600 degrees C

x Resistivity at 300 degrees C

140 . Resistivity at 100 degrees C o

130 o x

x

120

x

110 o

o .

100-

~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~—-90 x

80 o

x

70

60

50-

~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~o~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~—-o xx

40 o .

x .

30

o x

20

x .

10 .

0 Na K In Ga Li NaK Pb Sb Bi-Pb Hg Bi

(eu) (eu)

~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~—-Fig. 16-5 Electrical resistivity of various liquid metals at 100 degrees c, 300 degrees C and 600 degrees C.

Of all the liquid metals, sodium and potassium can be seen in Fig. 16-5 to have the lowest electrical resistivities, and mercury and bismuth the highest. It is interesting that NaK has more than twice the rseistivity of either sodium or potassium. The difference is attributed to a tendency of the sodium and the potassium to associate, a property of some liquid alloys that also affects other properties such as wettability, viscosity and heat of fusion.

Even though the efficiency of a DC electromagnetic pump may exceed that of an AC pump, the realtive efficiency of DC pumping versus AC pumping depends on the efficiency of high-amperage DC generators versus AC generators, and, for large scale work, the resultant advantage has commonly favoured AC pumping. The late Dr AC Barnes (ANL), however, developed a homopolar, high-amperage DC generator of high efficiency. It makes DC EM pumping preferable to AC pumping for some applications.

I think this may be starting to go a bit off the subject now and also I’ve noticed that the book was written in 1958 so will end there for now.

~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~-~~—15 Jun 2008, 15:40

## H.J.J. Braddick

I don’t think it’s quite what walter Wilkinson had in mind. There are nowhere near 4000 characters in it unless diagrams count for a lot more.

The transfer of Energy in Electromagnetic WavesIt is found, by calculating the work donein establishing an electro magnetic field, that the energy density in such a field is 1/8pye (eE2+uH2). if we consider a closed volume of such a field, in a medium in which there is no conduction current, it can be shown from Maxwell’s equations that the time-rate of change of the energy within the volume is equal to the surface integral of the normal component of the vector c/4pye (E x H) over the surface bounding the volume c/4pye (E x H) is called the Poynting vector (as we’ve discussed before) and can be used, in appropriate calculations, to represent the flow of energy per unit area in the field. But its properties are only proved for a closed volume and calculations must always be made using the surface integral of the Poynting vector over the boundaries of such a volume. The vector itself cannot be used in general as a measure of energy flow at a point: it would, for example, be wrong to use it to infer a finite energy flow over an area subject to crossed, steady, electric and magnetic fields. We could, however, use the Poynting vector to calculate the energy flow in a plane wave, for example by allowing the wave to fall upon an absorbing screen and drawing a volume bounded by two surfaces parallel to the screen, one in the wave field and one in the undisturbed region beyond it. The vector

E x His at right angles to each of the two vectorsE and Hand therefore lies in the direction of propagation. If, the maximum value of the electric vector is Eo, the energy flux is given by the time average of the Poynting vector and is c/8pye E2/0 per unit area.Electromagnetic Waves in SpaceIn order to study electromagnetic disturbances in free space or in an extended medium, we must adopt maxwell’s idea that a changing electric field is equivalent in its magnetic effect to a density of electric current, and since the electric and magnetic fields are at right angles, we must develope the equations in a three-dimensional form, conveviently by using vector notation.

The electric and magnetic fields in free space are connected by Maxwell’s equations:

a) div

E= 4pyep (c) *curl E = – 1/co aH/at }b) div

H= 0 d)curlH= 4pye/coj+ 1/co aE/at }Where

Eis the electric field, p is the charge density,jis the current per unit area, all in e.s.u., andHis the magnetic field in e.m.u.Electromagnetic Waves in Material MediaWhen electromagnetic waves pass through dielectric and magnetic media, their atoms acquire electric and magnetic polarization in the field of waves, and the problem must in principle be treated by the methods of the quantum theory. If, however, the frequency of the disturbance is not high, it is a good approximation to replace the free-space Maxwell equations by

curl E= – 1/co aB/dt = – 1/co d/dt (u*H*) }}

}

curl H= 1/co aD/dt = 1/co a/at (e*E*) }where u, e are constants depending on the magnetic and electric properties of the medium averaged over many atoms. This method is formerly possible at any frequency, quatum theory being used to calculate appropriate values of u and e.

The velocity of electromagnetic waves is deduced from equations (3.33) as co/(square root)ue.

15 Jun 2008, 16:26

## James Arnold Crowther

Electronic MassIt can easily be shown that a moving charge will act as if it possessed mass from the mere fact that it acrries a charge. Consider a point charge moving from a velocity v. This will be equivalent to a current element coinciding with the path of the particle and equal to ev, whwere e is the charge and v the velocity. The magnetic field due to the moving charge at a distance r from it in a direction making an angle 0 with the direction of motion will thus be ev sin 0/r2.

The energy in a magnetic field of strength H is I

_{H2/8rr per unit volume. Hence if du is a small element of volume at the point considered the magnetic energy in that element of volume will be I}/8TT (ev sin 0/r2)2 du.The whole magnetic energy in the space round the particlr will be the integral of this from the surface of the particle to infinity. To evaluate this, with the electron as centre describetwo spheres of radii r and r +dr and draw two radii making angles 0 and 0 +d0 with the direction of motion. If these are supposed to rotate about the direction of motion of the electron they will cut out from the sperical shell an annulus the volume of which is

2TTr sin 0 . rd0 . dr.

But the magnetic field is obviously constant throughout the space so obtained and hence the energy in the annulus is

I

_{/8TT (e2v2 sin2 0/r4) 2TTr2 sin 0d0dr = I}e2v2 sin3 0dodr/4r2.It can be shown on the electromagnetic theory that the above analysis is only true if the velocity of the particle is small compared to that of light (practically if it is less than one-tenth that of light). If the velocity of the particle approximates to that of light the ditribution of the electric field round the moving charge is altered in such a way as to increase the electromagnetic energy of the field and thus the elctromagnetic mass of the particle. The analysis is complicated and starting from different aasumptions as to the behaviour of the electron somewhat different formulae have been developed by different physicists.

15 Jun 2008, 17:45

## J.L. Ball

Electromagnetic RadiationsWhenever electric charges accelerate or decelerate disturbances are set up in the electric and magnetic fields around them. We say an electromagnetic wave has been generated. a useful and widely quoted analogy is to imagine an object floating on perfectly calm water. When the object is moved, disturbances are produced in the water. which cause surface waves to be generated which carry the disturbances outwards and away from the source. other objects floating nearby would experience these surface waves and be disturbed by them. we may infer that to produce this effect, the surface waves must be carrying energy. Electromagnetic waves also carry energy.

Energy and frequency of Electromagnetic WavesThe quantity of energy carried by electromagnetic waves depends on the magnitude (amplitude) of the disturbances in the electric and magnetic fields.

We define the frequency as the number of waves experienced per second. It is usually measured in “cycles” per second (c.p.s.) and the SI unit of frequency is the hertz (Hz), where 1 Hz = 1 cycle per second.

Electromagnetic SpectrumElectromagnetic waves can be produced by various maens resulting in different values of frequency. As well as having different frequencies they also have different energy values and different methods are required in order to detect them. The complete range of frequencies and energies is called the electromagnetic spectrum. Radio waves are at one end of the spectrum, having comparitively low frequencies and carrying little energy, while at the other end gamma rays have very high frequencies and are very energetic. Visible light rays have medium-value frequencies, while x-rays lie towards the high energy end of the spectrum. All these electromagnetic radiations travel very quickly; at roughly 186000 miles per second or the “speed of light”. At this speed radio waves can travel to the moon and back in less than three seconds. The symbol c is used universally to represent the speed of electromagnetic radiation. All electromagnetic waves travel at the same speed in a vacuum, and conveniently, their speed through air is almost exactly the same.

Rectilinear Propagation of RadiationElectromagnetic rays travel in straight lines; ie. they exhibit rectilinear propagation. They may deviate when passing through a junction between one medium and another; e.g. light is bent (refracted) on passing from air to glass, as in an optical lens. Refraction is not apparent with x- and gamma rays and for all practical purposes we may assume that these radiations travel in straight lines without deviation.

Because electromagnetic rays travel in straight lines it follows that if they are generated from a point source they will diverge, causing a reduction in the intensity of the radaition (i.e. in the concentration of radiation energy) as the distance from the source is increased. In other words, as we move further from the source of radiation, its effects become weaker. The exact way in which the reduction in intensity occurs is defined in the Inverse Square law.

15 Jun 2008, 18:59

## Duncan Donut

I’m sure there are lots of things I haven’t covered about electromagnetism but if you look at the following list, you can’t go far wrong:-

The fundamental laws of electricity and magnetism in integral form

Coulomb’s Law in surface integral form

No magnetic monopoles in surface integral form

Ampere’s Law in line integral form

Faraday/Lenz law in line integral for, the definition of the vector fields

E,B,H,D,PandM.The Divergence Theorem. Conservation of charge and the equation of continuity.

Stokes’ Theorem and the meaning of the curl.

The displacement current. Capacitor argument and compatibility with the conservation of charge.

Maxwell’s equations in differential form.

Vector differential identities.

The wave equations for the

EandBfields in a vacuum and a dielectric. The refarctive index.The general three dimensional plane wave and the wave vectore realtionship between

E,Band k. Intrinsic impedance.Polarisation of the photon. Linear eliptic and circular states.

The Poynting Vector and its properties.

The wave equations in an ohmic conductor, specialising to a good conductor. Skin depth.

Phase relations ata dielectric interface. Laws of reflection and Snell’s Law of refraction.

Amplitude relations interfaces. Fresnel’s equations and consequences.

15 Jun 2008, 19:20

Thanks for the notes.

15 Jun 2008, 22:03

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