ELECTRICITY – GOD’s Finger to Holds the World

1.1. The Beauty of Electricity

“Electricity and magnetism is all around us. We have electric lights, Electric clocks. We have microphones, calculators, televisions, VCRs, radio, computers. Light itself is an electromagnetic phenomenon as radio waves are. The colors of the rainbow in the blue sky are there because of electricity. Cars, planes, trains can only run because of electricity. Horses need electricity because muscle contractions require electricity. Your nerve system is driven by electricity. Atoms, molecule, all chemical reactions exist because of electricity.

You could not see without electricity. Your heart would not beat without electricity. And you could not even think without electricity, though I realize that even with electricity some of you may have a problem with that.“ [Walter Lewin]

1.2. Modern model of atom

Figure 1.1 – Modern Picture of Atom

Table 1.1 - Property of an atom

	Neutron	Proton	Electron
Diameter size (m)		1.2×10-15	5×10-11 to 5×10-10
Mass (kg)	1.675×10-27	1.673×10-27	9.109×10-31

1.3. History of electricity

Electron, name from a Greek word, means amber. As reported by the ancient Greek philosopher Thales of Miletus around 600 BC, it was known that if we rub amber that it can attract light objects such as pieces of dry leaves and hair. So that's where electricity got its name from.

In the sev-sixteenth century there were more substances known to do this, for instance glass and sulfur. And it was also known and written that when people were bored at parties that the women would rub their amber jewelry and would touch frogs. The frogs would start jumping of desperation, which people considered to be fun, but they not understanding what actually was happening to the amber nor what was happening to the frogs.

In 1733, C. F. du Fay proposed two varieties of electricity that cancel each other, and expressed this in terms of a two-fluid theory. When glass was rubbed with silk, du Fay said that the glass was charged with vitreous electricity, and, when amber was rubbed with fur, the amber was said to be charged with resinous electricity. Let's call one A and the other B. It was known that A repels A and B repels B but A attracts B.

Still in the eighteenth century, it was Benjamin Franklin without any knowledge of electrons and protons who introduced the idea that all substances are penetrated with what he called electric fluid, electric fire. And he stated if we get too much of the fire then we are positively charged and if we have a deficiency of that fire, then we are negatively charged. He introduced the sign convention and he decided that if we rub glass that that is an excess of fire and he called that therefore positive.

We will see later that why this choice he had fifty percent chance is extremely unfortunate but we have to live with it. So if we take this fluid according to Benjamin Franklin and bring it from one substance to the other, then the one that gets an excess becomes positively charged. Automatically as a consequence of that the one - from which we take the fluid - becomes negatively charged.

1.4. Electric charge

Charge is an intrinsic property of partikel or matter. Charge have been quantized and comes in multiples of individual small units called the elementary charge, e, approximately equal to 1.602×10⁻¹⁹ Coulombs. The proton has a charge of e, and the electron has a charge of –e.

A neutral atom has same number of electron and proton, so the charge is 0. If we take one electron off, the atom will become a positive ion. If we add an electron then, the atom will become a negative ion. Remember, we can't add or taking off a proton from an atom.

The electric charge is a fundamental conserved property of some subatomic particles. This is the same as the idea of Benjamin Franklin. We can't create charge. If we create plus then we automatically create minus.

1.4.1. Electric charging

The question is “how can we manipulate or engineering the electricity?”

That because we are able to separate positive and negative charge from each other. This process called charging and there are three methods to do that.

1.4.1.1.   Friction

From the history above, people has been known that friction can produce positive and negative charge. Charging by friction can happen since the two objects are made of different materials, so their atoms bounded their electrons with different strengths. As they pass over each other the electrons with weaker bonds are “ripped” off of that material and collect on the other material.

1.4.1.2.   Conduction

Charging by conduction is also called by contact. The principle is when we contact a neutral material with a charged material, the electron will be transfered and neutral material will become a charge material. But even if the material not make a contact and just close enough to let the electron jump from one material to another material, that is also conduction

With conduction we will get the same type of charge. So, If we conduct with positive charged, we will get a positive material. And if we conduct with negative charge we will get a negative material.

1.4.1.3.   Induction

We can also charging a material without contact or transfer of electron. This prosses called induction. As in conduction, type of material will determine the behavior of induction.

1.4.2. Electric charge behavior

As we know before, same type of charge will repel each other, and different type of charge will attract each other. But, do you know, what it is that makes us easy to charging or not?? The answer is the type of material. There are two type of material based on it’s electrical property.

1.4.2.1.   Conductor

Conductor materials have moveble electrons, so, it is easy for the electron to move from one atom to another atom. Electrons of conductor material will move when an electric potential difference (measured in volts) is applied across separate points on the material.

Because of easy movement electron, it is easy to charging the conductor material by conduction method. The opposite, it is more complex process to charging the conductor material with induction method.

Figure 1.2 – Conduction and induction of conductor material

1.4.2.2.    Insulator or non-conductor

The electrons of insulator material are tightly bound and localized in direction of chemical bounding. So, it is hard for the electron to move from one atom to another atom. Perferct insulator does not respond to an electric field and completely resists the flow of electric charge. But in real, there is no perfect insulator, so almost of the material are semiconductor material.

In practice, the insulator can be polarized by an applied electric field, and it called dielectric material. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in a conductor, but only slightly shift from their average equilibrium positions causing dielectric polarization. Therefore, dielectric materials with high dielectric constants (not easy to polarized) such as glass, paper or Teflon are considered as good electrical insulators.

Dielectric property makes easy to charging non conductor material by induction method. Rather than that, it is more complex process to charging the insulator material with conduction method due to only the specific areas that actually touched would show any change in charge.

Figure 1.3 – Conduction and induction of insulator material

1.4.2.3.    Spark phenomenon

An electric spark is a type of electrostatic discharge that occurs when an electric field with strength exceeds the dielectric field strength of air. This exceeded field strength causes an increase in the number of free electrons and ions in the air and temporarily causing the air to become an ionized electrically conductive channel. This process producing a brief emission of light and sound, and that usually we call spark.

Electric sparks occur in or near many man-made objects. Some of them are small and some of them are large. Sometimes it can happen by accident, and sometime it is by design. Lightning is an example of an electric spark in nature. A continuous discharge of electric current through a gas is an electric arc.

1.4.3. Conservation of charge

The total electric charge of an isolated system remains constant regardless of changes within the system itself. Charge cannot be created. If we create plus then automatically we create minus. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the net change in charge density ρ within a volume of integration V is equal to the area integral over the current density J through the closed surface S = ∂V, which is in turn equal to the net current I:

Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:

The charge transferred between times t_i and t_f is obtained by integrating both sides:

where I is the net outward current through a closed surface and Q is the electric charge contained within the volume defined by the surface.

1.4.4. Electroscope - a principle to measure charge

We will use various instruments to measure charge in a quantitative way and one of the instruments that is very simple, is called an electroscope. In general it is just a conducting rod (such as aluminum, metal) with two pieces of tinsel at the end. The pieces of tinsel usually from aluminum foil. And often there is a nice knob, so if we touch or bring near enough to knob with a charged object, then because the rod is conductor, this can conduct the charges.

If we touch it with an object which is positively charged, then this electroscop will become positively charged. If I touch it with an object which is negatively charged it will become negatively charged. If we induce the knob with positive charged, the knob will become negative charged and the the pieces of tinsel will become positive charged. At the end, we will see that the two very light pieces of aluminum foil will repel each other and shows a certain angle, and the more charge there is the larger that angle.

Figure 1.4 – Electroscope and example of measurement

1.5. Electric force

It was Charles Augustin de Coulomb, French physicist, who did a lot of research on this in the nineteenth, eighteenth century actually. He found a special relationship between two charges. It was first published in 1785 and was essential to the development of the theory of electromagnetism. Before it was published, other researchers have been insights into aspects of Coulomb's law. In 1767, Joseph Priestley of England conjectured that the force between charges varied as the inverse square of the distance.

Coulomb's law or Coulomb's inverse-square law is a law of physics describing the electrostatic interaction between electrically charged particles. Coulomb found that the force is proportional to the product of the two charges, times a constant, which nowadays we call Coulomb's constant, K, and then divided by the distance between these charges squared.

Now let's try a little bit more quantitative. If we take two charges and we use for charges the symbol q₁ and q₂. They are separated by a distance, r, and the unit vector in the direction from one to two that we called r roof _1,2. (The roof stands for unit vector). If these charges are equal, both minus or both plus, then charges will repel each other. The F_1,2 is the force on two due to number one. Since action equals to minus reaction, force F_2,1 is equal to F_1,2 in magnitude but a hundred eighty degrees, or it is in opposite direction.

Figure 1.5 – Electric force between two charges

Where:

q= charge [Coulomb]

r = distance [m]

K= coulomb’s contant = 8.987551787 × 10⁹ [Nm²/Coulomb²] = 

1.5.1. Superposition

If there is three or more charge, we can use the superposition principal. In other time we will discuss about that.

1.5.2. Electricity force vs gravitational force vs nuclear force

Look at what Joseph Priestley found and see equation (1-1), I suddenly remember to the Newton law’s of gravitation.

Figure 1.6 – Gravitational force between two mass

Where:
m = mass [kg]
r   = distance [m]

G = gravitational contant [Nm²/kg²] = 6.674 × 10^-11 [Nm²/coulomb²]

And if we compare electricity & magnetism with mechanical, thereby comparing electricity with gravity, we will see that electric forces are way more powerful than gravitational force. Let’s see that is by taking two protons which are a distance D apart. As they have the same charged, they will repel each other, because of electric force. Remember of Table 1.1, we know that the proton have mass. Because gravity always attract each other, so it will become force that opposite to the electric. Now, the question is “which one is more powerfull?”

Figure 1.7 – Example of force acting on protons

To answer the question, let’s use equation (1-4) and equation (1-5) with the data from Tabel 1.1:

From the result above, we found that the electric force is thirty-six orders of magnitude more potent than the gravitational attraction. If these were the only forces that acted on the protons and you bring them in the nucleus, which has a size of only ten to the minus fourteen meters, then the acceleration that the proton will experience is the electric force divided by the mass of the proton. If there is two protons in an atom, then the electric force that repel the protons each other have ratio about twenty-six order of magnitude higher than the gravitational acceleration on earth.

As we know the gravitational attraction is thirty-six order of magnitude lower than repelled of electric force, ‘what kind of force that holds nucleus together?’ There must be such a tremendous force on these protons. Well, the answer is the nuclear forces that holding them together. We will not discuss about nuclear force on this topic, so, just leave it alone for now.

So what holds our world together? Well …. :

i)        On the nucleus scale (about 10^-14m), nuclear force are very important.

ii)       On an atomic scale up to thousands of kilometers, it's electric forces that hold our world together.

iii)     But on a much larger scale, planets and stars and the galaxy, it is gravity that dictate the behavior of the universe.

After we know about that, we may say, “That's very inconsistent with what we have learned in Figure 1.7!” Yes, however, most objects are neutral or very close to neutral and so if you take the earth it is very unlikely even that the earth as a whole would have a charge of more than ten coulombs (that probably is already an exaggeration). So, if we put the earth with ten coulombs and then we put minus ten coulombs, so they will attract each other, but given their distance, it's almost nothing. The electric force on that scale is negligibly small. But of course, at that scale, the force of gravity wins, because of their massive masses.

In this particular case, which we take the earth and the moon, the gravitational force wins over the electric force by twenty-five orders of magnitude. So even though our immediate surroundings are dominated by electric forces, including our own body for that matter, the behavior of the universe on a large scale is dictated by gravity.

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