2.4 Potential Difference

Previous sections:
1. Introduction
2. Electrostatic
2.1 Coulomb's Law
2.2 Gauss's Law of electrostatic
2.3 Electric field in materials

2.4 Potential Difference

Recalling that for electrostatic, the electric field must satisfy the below two equations at all points of space and time.

∇.D=ρ

∇xE=0

In this section, we shall set out to prove the second equation, which reads "the curl of E is equals to zero". As mentioned in section 2.2, the symbol that looks like an inverted triangle, ∇, is called nabla and it is actually a vector (d/dx, d/dy, d/dz). We shall defer the mathematics to later and try first to understand the physical significance of ∇xE=0.

The past few sections described, in general, the behaviour of electrical charges under the influence of an electrical field. Up to this point, we would already know that a positive electrical charge moves along the 'force lines' of an electrical field. The electrical field 'points' from a positive charge, say in point A, towards a negative charge, in point B. This is equivalent in saying that there is a potential difference between point A and B, which moves the electrical charge. Although the word 'potential' is common among science and engineering students, many take this word for granted and do not really understand what it means. Therefore, before going any further, I will attempt to answer the following two fundamental physics questions regarding 'potential'. However, if you are already an adept physics student you can skip this part and go straight to the section on 'potential energy' below.

What is potential (from physics point of view)?

In physics, it is said that energy is conserved. No energy is created or destroyed. It is only changed from one form to another. When you throw a ball towards a wall, it has kinetic energy. When the ball hits the wall and bounces back towards you, portion of the kinetic energy is converted to sound (that is why you will hear a 'thud' when the ball hits the wall); part of the energy is converted to heat due to the friction of the ball with the wall and air (although this is small); and some of the energy is also converted to heat due to atomic collisions within the ball when it deforms as it hits the wall (amount of energy converted here depends on the material of the ball). The total energy of the ball before and after the collision with the wall is exactly the same.

But a peculiar case happens when we lift a heavy object against gravity. Obviously when we lift an object against gravity, we need energy. But if energy is not destroyed nor created, then where does the energy go to? It is not sound or heat or any kind of energy that we can clearly measure. But the energy is clearly not lost because if we now release that object, it picks up speed, gains kinetic energy and thus falls towards the floor. The energy is actually 'stored' within that object and we say that the object has gained potential energy, i.e. potential to do 'work' or release energy.

How does a potential 'do' work?

We can never know the absolute amount of potential energy that an object has, we can only know or measure the difference. For example, when we lift an object a certain distance above the ground, we can only know that this object has gained a certain amount of potential energy, proportional to the distance it has been lifted. But what is the absolute energy it has? How much potential energy does it have in the first place? Is it possible that even before we lift the object, it already has a lot of energy stored in it? We can never know. This is because we cannot measure or observe this 'stored' energy directly. Therefore what is important is the magnitude of the difference of the energy, not the absolute value of it. Because we are only concerned with the difference and not the absolute value, it presents us with a flexibility to define what potential energy is.

If we now reverse the process i.e. we release the object from a certain height and let it fall to the ground. This object will release the 'stored' potential energy, which is equivalent to the difference of potential energy between the height it was released and the ground. In other words, an object will attempt to do work to release the 'stored' energy when there is a potential difference. This difference can be a postive or a negative one, depending whether it is A - B or B - A. It is, however, of no real physical significance whether it is positive or negative. In practice, it is common that we define the value of 'potential' mathematically such that energy is released when the object move from a high potential to a low potential, i.e. when A - B > 0 then energy is released and work is done by the system; but when B - A > 0, work needs to be done on the system instead. (although students should take note that there are special cases where it is defined that energy is released when moving from low potential to high potential, this is only a change of definition and does not affect what we observe in the real world).

A way to imagine this convention is to to take the analogy of river flowing from the mountain tops to the sea. River will always flow (i.e doing work) from a higher place to a lower place (i.e. high potential to low potential). When the surface is flat, the water does not flow (i.e. no potential difference)

Potential Energy

If an electrical charge move from point A to point B under the influence of an electrical field, we could have as well said that this is due to a potential difference between A and B. This potential energy must have been stored when we moved, for example, a positive electrical charge against the electrical field. Just as when we lift a ball off the ground and release it, the ball would fall back to ground; so would the electrical charge if moved against the electrical field and then released, it will move back to its original position.

This stored potential energy due to moving a charge against electrical field can be calculated by using the simple equation:

Energy = Force x Distance.

However, if the force acts along a curved line, then the distance which the force acts may then not be trivial to calculate. We can still do this by assuming that a curved line is formed by a series of small arrows. The smaller the arrows, the closer it matches to the curve. In this way, we can calculate the energy that is stored in an electrical charge by tracing the force, F, along the small arrows. Energy is now equal to force x distance, i.e. F . dx where dx is the length of the very small arrow (Note: both F and dx are vectors. By taking the dot product of F and dx, we find the component of F in the direction of the small arrows.) When dx becomes infinitesimally small, this becomes an integration: ∫ F. dx

but F=qE, therefore

q ∫ E. dx = -Energy (to move from A to B). The negative sign is to indicate that work is done when moving an electrical charge against electrical field. As described above, this is just a convention such that we all agree energy is released when a charge moves from high potential to low potential points.

Energy/q = - ∫ E. dx
V = - ∫ E . dx

Therefore, potential difference is just the energy per charge. Now bringing the dx over the other side of the equation and considering only a small change in potential leads to:

- dV / dx = E

In 3-dimension, d /dx becomes (d/dx, d/dy, d/dz) which is equivalent to ∇. This suggests that E=-∇V, where ∇V is read as grad V.

Now, it can be shown (mathematically) that a charge does not gain any net energy by moving from A to B and then back to A again. E.g. the charge gains energy when moving from A to B and releases this same amount of energy when going back from B to A. We call this a conservative field, i.e. the net energy gain depends solely on the end points (initial and final position). You can take an electrical charge on the planet Earth, take it to the moon and the bring it back to Earth but at 1 cm away from the original position - the net energy that it gains or loses is still due to that 1 cm distance. The fact that you had brought the charge to the moon and back makes no difference at all!

So if we move an electrical charge from A to 'somewhere' and back to exactly A, no net energy is gained (or equivalently, no work is done). Mathematically, we write this as

∫ E. dl =0

where the integration is taken over a closed loop. A loop is like a line where the beginning point is the same as the ending point, therefore there is not net energy gained. From Stoke's theorem we obtain ∫ E. dl = ∫∇xE dl =0, i.e ∇xE = 0, which is what we set out to prove.

At first glance, this seems like an immensely stupid equation because we are calculating the energy to bring a charge from A to B and then back to A again, which is essentially zero. It sure sounds more useful if we are actually calculating the energy from point A to some other point in space. But the purpose of the equation is to help us in characterising electric field in static conditions, it is suppose to give us a set of 'criteria', if you will, to fulfill if the electric field is static and that is exactly what the equation does. The physical meaning of the equation is to say that in the case of electrostatic, the electrical field is conservative - that is the potential difference is independent of path (travelled by the charge) and only depends on the displacement (initial and final position) of the electrical charges. We will see later that this is not always the case. It is useful to note that the statement "Electrical field is conservative" also gives information on how to calculate the potential difference between two points.

So the equations ∇.D=ρ and ∇xE=0, together with the bounday conditions, which we will talk about in the next section, are all the information you need to know about electrostatic field.

Kirchoff's Voltage Law

As a final note, it is important to note that the above relates to Kirchoff's Voltage Law, which states that the voltage drop in a (closed) loop is zero. This is a mathematical consequence of ∫ E. dl = 0. If we have a battery, however, then the electrical field is no longer conservative, the situation is no longer considered as electrostatic and therefore this equation is no longer true in such situations.

辩手，评判们：是谁赢了这场比赛？

我在辩论界已混了至少15年。虽然 ，还是有比我更老的前辈，但是我看过的辩论比赛绝对不少，可说是经验不浅。而这么多年来令我最讨厌的就是看到辩论员们辛辛苦苦为一场比赛准备了这么久，却被误判而输。

所以，我恳请大家 -- 所有辩论老前辈，现任以及过去的辩手或是评判帮帮手。帮我看一下这一场“辩论赛”到底是谁胜了？是不是代表Allah专利权的那一方获胜？若是，我 “切”！！！

Principles, not sensitivities!

The best speech that I have seen so far related to the recent "Allah" ban in Malaysia was not from PKR, DAP or PAS. Surprisingly, it's from an UMNO member. And I'm not being sarcastic.

You can read Tengku Razaleigh's full speech here. The speech was given at the Institute of South East Asia Studies Regional Outlook Forum 2010 at Singapore on Jan 7 2010.

The following are the arguments that I am most impressed with, "...a government whose primary response to a public issue is sunk in the elastic goo of “sensitivities” rather than founded on principle..." and "...It is about doing what is right rather than protecting arbitrary feelings. If feelings diverge from what is right and just, then it’s time to show some leadership."

A leadership that is based on "sensitivities" of a particular group will always flip-flop on his decisions, contradicting constitution and law on the way of doing so. A leader whom is not guided by principles, will allow himself/herself to be led by the nose.

If our PM's leadership was founded on principles rather than to satisfy his need to stay in power or to satisfy the sensitivities of a group of extremists, this is what he would have said,

"I understand that the recent court ruling on the usage of Kalimah "Allah" has caused concerns among various people, Muslims and Christians alike. First of all, I would like to assure everyone that everybody has the freedom and right to practice their own religion. No one should force someone's religion onto another, be it Islam or Christianity.

Any religion, and especially Islam, emphasizes peace and harmony. Muslims are compassionate. And Muslims must more so show this virtue during the time when some of us have a slight disagreement with our Christian brethren. Let us not forget that they are also our fellow countrymen and neighbours, whom we have lived together in harmony for so many years. Everyone deserves compassion and patience from a Muslim, what more if they are our fellow countrymen? Therefore, we must refrain from any violence act and engage in a dialogue to solve our differences, as Nabi Muhammad S.A.W. would have.

The usage of Kalimah "Allah" by non-Muslims though may be an issue, it is neither the most important issue facing Islam today nor is it the most important teaching from the Quran or Bible. There is no point in getting the Kalimah right, but indulging in corruption, ignorance and violence at the same time. It is an issue. I am not saying it isn't. But it is not the most important issue facing the Islam faith or the Muslims of Malaysia right now. I assure you, that we will seek a solution to this, and we shall seek it through inter-faith discussions and forums, not through violence.

The ruling is now under appeal. I urge to let the court process to take place and respect the judge's decision. There is a reason for the court and the law to exist. Although it may not be perfect, we must respect the process and to amend the law through the right process. And that is through the Parliament, not through the streets or violence or by inciting hatred. In this case, as the leader of the majority party in the Parliament, I shall take the lead in proposing an amendment to the relevant laws to rectify the problem. I shall do this, only after in consultation with various parties and after sufficient inter-faith dialogues have been made. Meanwhile, let us be patient and respect the judge's decision.

Therefore, I urge everyone to be calm and patient during this time. Show what real Islam is about. Show what being a Malaysian is about."

This, is what I would said if I am the PM. He should have been neutral. But instead, he chose to blatantly side with the Muslim extremists.

雪州513

翻看着以前的帖子，我发现我在3个月前早已对上星期在雪州所发生的一连串事件做过类似的推测：

1。在雪州制造骚乱（迷你513）
2。内政部长利用“牛头”事件来合理化这次的示威。

两个，全中！

我进一步推测，近期内警察的调查结果会是：放火烧屋的恶徒，不是回教极端份子，而是一些亲反对党的非回教徒。从而，又再把责任推向给反对党。

希望我的推测是不对的。

Great Britain covered in snow!

Can you recognise this?
It's Great Britain covered in snow (actual satellite picture).
I'm at the south east corner.
Freeeeeeeeeezing cold...........

Ruin and run...

Perhaps, there's no one to blame for Malaysia's plight. It's all due to bad pronunciation really:


Najib: Run the country to the best of your ability!

Ministers: Ruin the country!

Najib: No, I said, "Run", not "Ruin"

Ministers: Yeah, ruin! not run.

Najib: Run!

Ministers: Ruin la. I said ruin what.

Najib: Run, Run, Run! I said run the country!

Ministers: Ruin, Ruin Ruin. We'll ruin the country!




Police: I warn you first, you can only have protest. After that, run, or I'll catch you!

Mat Rempit: Ok. After protest, ruin. Find church to ruin. Got it.

Police: No. I said run.

Mat Rempit：Ruin?

Police: Run. R-U-N. Rrrrrrun.

Mat Rempit: I heard you the first time. Ruin.

Police: Run!! I said "run". It's R-U-I-N without the 'I'.

Mat Rempit: I no ruin? how can? then who ruin la?

Police: I said run. If not, I'll put you in lockup.

Mat Rempit: Ok Ok. Flip-flop lagi. I'll ruin. I don't want to stay in the lockup.

Police: No. I meant run. After that, RUN!

Mat Rempit: Ooooh ok. Now I get it, after I ruin, I run. Roger that!

钱不是万恶之源。。。

它，才是万恶之源。

万恶当然不是指所有的恶，而是指 "数量极多，而且品种繁复的恶行"。我方认为世上穷凶极恶的恶行都来自xxx。

家庭暴力，是为了钱。但，再怎么凶，家庭暴力不是恐怖主义；
恐怖主义，是恶。但，再怎么残忍，恐怖主义不是为了钱；
麻原彰晃，既是恐怖主义也是为了钱。但他不是霸权；

可是xxx，比他们都还恶。
它，聚集了霸权、金钱、以及恐怖主义于一身。
它为了钱和权，无所不做。
它是贪、嗔、痴。
它“异化了人与钱之间的关系”。
它是万恶之首的淫。

可是它不是钱。它来自马来西亚。

A gifted child...

Son: Dad, I want to quit school.

Me: What?! But why?

Son: School is so boring. They are teaching calculus, which I already knew since I was 6, and they are still learning Newtonian physics. When are they going to start on quantum mechanics?

Me: Yes, you are a gifted child. But do stay in school, dear. If you find the academic side of the school is boring, try joining student organisations, like the Chinese Language Society or debate team.

Son: Like what you did when you attended high school?

Me: Yes. You can learn about people relationship, people management, organisational skills but most of all it is fun! You could also do some charity work in the local community. By helping the poor and the weak, you get to see things from other people's point of view and it will change your life. You could also play some games, mix with people, go after girls, you know, those things that other high school boys do?! (laugh)

Son: But what's the point?

Me: What's the point of going after girls? (*Gasp*)

Son: No, dad. (=.= "') I know about going after girls. I meant, what's the point of learning people skills, etc ...

Me: Great to hear you are interested in girls already (*wink*). Well, there's a lot more to school than just knowledge, you know. And that's certainly true as well when you step into the society to work, which will happen soon enough. To make the right decision, you must learn how to appreciate the people around you, the culture and history. To realise a plan, you must make people to work with you. You don't expect to get everything done by yourself, do you?

Son: Didnt' Einstein developed theory of relativity all by himself?

Me: No. First of all, without Newton and all the subsequent scientist's groundbreaking work in gravity, there would be no theory of relativity. They were the necessary foundation to Einstein's work. Let's not forget that he had to rely on Eddington to verify his theory. And most important of all, Einstein was not just a physicist, he was also actively involved in politics and was influential in both the World War 1 and 2.

Son: Really? I see.

Me: Your knowledge must have a positive impact to yourself, to the people around you and ultimately to humanity, but you would not be able to do that if you do not first appreciate and respect the people around you. What good is knowledge if it doesn't help yourself and those around you?

Son: Does it always come in that order? Self, people around me, and then humanity? Sounds a bit far-fetched don't you think? Humanity, eh?

Me: Your sphere of influence grows in that order - you first influence yourself, the people around you and then, if you are lucky, humanity. But the importance is in the reverse order. Always place others before yourself. You will never know though, that some day you may be some one great and influential. But even if you are not the leader of the world, you are always important to me, to your family and those around you.

Son: Thanks dad.

Me: You are welcome. Remember, stay in school. Spend the extra time with friends and learn more about people, it's much more complex than quantum mechanics and string theory, trust me on it. There's no hurry in learning quantum physics and string theory. You can always accelerate your academic skills after high school when you start your university education. So what do you think? You feel better about school now?

Son: I guess so. I will check out the notice board tomorrow to see if any student project interests me.

Me: Good. Now, go out and play with your friends.

Son: OK. But I think I would go to my room and finish the book "The strange theory of light and matter" by Feynman. I am already at the last chapter. Love you, dad.

Me: Love you too.

Malaysian Job

It took half a dozen people in "Italian Job" to pull off a 35 million dollar heist;

It took almost a dozen professionals in "Ocean's eleven" to steal millions from casinos;

But all it took was TWO Malaysians to steal 2 multi-million dollar jet engines from a high-security Malaysia Air Force base in the middle of the busy Klang Valley, smuggle it out of the country, and somehow find a buyer for ... jet engines?

Screw Hollywood. The real deal is in Malaysia!

0, 1, 2, smile ...

Q: How many economists does it take to screw in a light bulb?
A: None. If the government would just leave it alone, it would screw itself in.

Q: How many gorillas does it take to screw in a light bulb
A: Only ONE, but it sure takes a shitload of light bulbs!

Q: How many Malaysians does it take to screw in a light bulb?
A: TWO. One to dismantle it, put it on the forklift, move it to the truck, evade all security personnel, drive the truck all the way to the port, move it into the container, lie to the customs officers, and get the engines offshore. The other just sells them.

Oh wait, I was describing jet engines, not light bulbs...

Allah must be laughing now...

Allah (whichever God you might refer to) must be laughing so hard now that His teeth is falling off from the sky in the form of meteor showers tonight.

I am pretty sure Allah can understand more than one language, so He must be bemused by the people who are worried that He could not understand you if you do not address Him in the right language. He must be even more bemused that some of His followers actually got confused when a different name is used to call Him.

I am neither Christian nor Muslim, but I am pretty sure that "what is the correct name to call Me" is the last priority for God's teachings. If it isn't, you should reconsider your religion because it sounds too damn easy to go to heaven.

Certain quarters of Christians and Muslims felt insulted. I think Allah aka Tuhan aka God should be the one that feels most insulted because of all His teachings passed down over the centuries, we were most concerned with what to call Him. I am sure this make a heck of a religion.

My mentor in high school once told me this, "There will always be problems in your life. A beggar and a businessman millionaire have the same number of problems. But the level of problems faced by these two people is what distinguished them. One is of higher stature, the other is not..." I cannot help but to think that this applies to religion too.

(in reference to the recent uproar by some Malaysian Muslims against the usage of 'Allah' by Christians to refer to the Christian God)

2.3 Electric field in materials

Previous sections:
1. Introduction
2. Electrostatic
2.1 Coulomb's Law
2.2 Gauss's Law of electrostatic

2.3 Electric field in materials

So far we have considered the electric field in free space. Obviously, if we now consider the electric field in materials (insulators or conductors), things will be quite different.

In the previous section, we shown that ∇.E=ρ/ε. Let's call this ρ as free charge since it represents the electric charge that is 'free' to move around (note: only free charge contributes to electrical current). Let us now assume that when we apply an electric field to the material, the material will modify the electric field either by strengthening it or weakening it, depending what kind of material it is. Let us represent this effect by introducing an additional charge, called the bound charge, ρ_bound. (These charges are not free and are 'bound' to the material and they cannot freely move about to generate electrical currents.)

One of the ways to imagine bound charge is to consider applying an electric field to a perfect conductor. Assume that the material consists of many electrical dipoles, i.e. opposite charges separated at short distance. (Such dipoles may exist, for example, in molecules with ionic bonding. The electrical field will displace the positive and negative ions slightly to create a dipole.) Now, further assume that these dipoles are not free to move about. They are fixed or bounded to the material. They can only rotate about their axis. What the applied electric field would do to these dipoles is to align them along the electrical field lines with the head of one dipole lining up behind the tail of the other dipole (refer to the diagram below). The result of this 'bound charges' aligning is that the internal electric field cancel each other out (due to the positive and negative charge lying close to each other). This result is important, so remember it: Electrical field inside a perfect conductor is zero. What happens if it is not a perfect conductor? Then, the dipoles cannot align perfectly and the electric fields will attenuate/diminish but it will not be completely cancelled out. You may also ask, what allows us to make such assumption about the electrical dipoles? Nothing, except that experimental results seem to suggest that such assumption is reasonable. As with previous, science is always about suggesting a good assumption to explain the experimental results.

Therefore, in the presence of any material (insulator or conductor), we modify the equation to become ∇.E=(ρ+ρ_bound)/ε to include the bound charges in a material. Having different kinds of charges (bound and free) in the equation is very confusing, this is why in Maxwell's equation all charges always refer to free charges. In order to be consistent with this, we rearrange to 'get rid' of the bound charge in the equation, i.e.

∇.εE - ρ_bound = ρ ;

∇. (εE + P) = ρ ; where ∇.P= - ρ_bound

∇. D = ρ ; where D = εE + P

The polarisation vector P, is the electric dipole moment density. By considering that an electric field causes dipoles to re-arrange in materials, one can calculate that the actual effect an electric field has on a material is to generate a 'surface charge' and a 'volume charge' which is related to P. You can refer to many textbooks on how this is calculated, or you can take my approach, which is just to assume P is a value (like kilograms is for weight) to indicate how much the electric field is affected by the material.

Since the electric dipole is induced by E, we may suspect that P is related to E too, and this is indeed the case. However, the relation may not be a linear one. In most cases we can assume it is linear, i.e. P=kE. But we write P=εχE, where ε=permeability of free space (as usual) and chi, χ=electric susceptibility.

Then D = εE + P = εE + εχE = ε(1+χ)E = ε . ε_r . E ;
where ε_r = (1+χ) is the relative permeability

If ε_r is independent on position, i.e. the same throughout the material, then the material is said to be homogenous. If it is homogeneous, then in general, D = ε . ε_r . E is in matrix form where D and E is a 3 x 1 matrix and (ε . ε_r) is a 3 x 3 matrix. If only the diagonal elements of (ε . ε_r) is non-zero, i.e. the relative permeability is only dependent on the principal (x, y and z) axes, the material is called biaxial, or isotropic:
Dx = ε . ε_r11 . Ex
Dy = ε . ε_r22 . Ey
Dz = ε . ε_r33 . Ez
(where the number indicates the position in the 3 x 3 matrix)

Furthermore, if ε_r11=ε_r22, then the material is said to be uniaxial.

In summary, in the presence of (any) material, the electric field will be different than from the free space and this difference is accounted for by using ε_r, the relative permeability. The equation that relates relative permeability to the electric field, E and displacement field, D is

D = ε . ε_r . E.

But this equation can be confusing sometimes. We can essentially move the relative permeability to other side of the equation and it will now look like this: E = D / (ε . ε_r ). So does the relative permeability serve to modify D or E to account for the presence of a material? If, for example, a dielectric material is placed between two conductor plates (like a capacitor), a constant (electric or displacement?) field will be generated across the dielectric material. What happens at the interface between free space and this dielectric material? Does the displacement field or the electric field change due to the presence of this material? Or both? Although we can use sheer mathematics to find out the answer, it is much more meaningful if we instead rely on our intuition to understand why and which should be the answer. Obviously if both D and E change, and by the same amount, then there is no difference between the two quantity, so this is not allowed. The equation tells us that D and E is related by the permeability, but it does not tell us which is the constant and which is being 'affected' in this case. But if we pay attention to the words I have used so far, I have always said "the materials affect the electric field" and NOT the displacement field. This is a very reasonable statement, since inside a material, especially a conducting one, the charges are BOUNDED, NOT FREE. Displacement field's relation to the charge as indicated by Maxwell's equation ONLY refer to free charges. The free charges, accumulated at the surface of the conductor plates, are constant and therefore D should be constant. The electrical field, on the contrary, is related to the free charge AND the bound charge inside the material. And therefore it is the electric field that will be affected in the presence of a dielectric. (note: there are no free charges INSIDE a conductor but free charges can reside at the SURFACE of a conductor)

In short, the difference between D and E is that "D is the field due to the free charge only" and "E is the field due to both the free and bound charge", the effect of the bound charge is included indirectly through the relative permeability. The quantity D is introduced so that we can make Maxwell's equation look much neater, i.e. always only referring to free charge only. But the usefulness of this displacement field will be more obvious when we disscuss the dynamics of electromagnetism.

Although we have introduced many terms like the polarisation vector, the electric susceptibility, and the relative permeability, it is the relative permeability that is most commonly used to describe the effect of materials on electric field. However, we must always bear in mind that relative permeability is obtained through a series of assumptions. There will be time when we cannot use the relative permeability but instead must use the 'original' equation that contains the polarisation vector or susceptibility, especially for the case of describing in depth behaviour of materials. As a special case, consider a perfect conductor. What is the relative permeability of a perfect conductor? Because D = ε . ε_r . E and E is zero inside a perfect conductor, D will always be zero inside a perfect conductor but this is not true! If we instead use D = εE + P, then when E is zero inside a perfect conductor, D = P. The polarisation vector represents the contribution from the bound charge and thus D is non-zero even in a perfect conductor. Remember, relative permeability is useful because it is a GOOD APPROXIMATION to the 'overall' behaviour of electrostatic systems but it does not work all the time.

New Year Resolution for 2010

My 10 New Year Resolution for 2010:

1. Publish at least 2 scientific journal papers, with at least 1 in high impacting factor journals.

2. Finish the book on introduction on quantum mechanics and the chapter on density functional theory (this should be easy, since I'm already half-way there!).

3. Finish reading '1434'.

4. Read another (non-academic book).

5. Complete project Ascension (my little project on a motivational and skill course for PhD students)

6. Complete my little online book on EM.

7. Exercise, exercise and exercise - regular exercise per week, i.e. at least 3 times a week.

8. Play Mass Effect 2

9. Purchase original Starcraft 2 DVD. (yeah, noticed the difference with no. 8?)

10. Travel to Europe.