Thursday, December 26, 2019

Unizor - Physics4Teens - Electromagnetism - Unit of Electric Charge

Notes to a video lecture on

Electric Charge Unit - Coulomb

Since electrons are the carriers of electricity, we can measure the amount of negative electricity in any object as the number of excess electrons in it, that is the number of electrons that do not have a proton to pair with.

In case of deficiency of electrons, we can measure the amount of positive electricity in any object as the number of excess protons, that is the number of protons that do not have an electron to pair with.

The problem with this way of measuring the amount of electricity is that this unit (amount of electricity in one electron or one proton) is very small and inconvenient for practical matters.
For this reason physicists use a larger unit of electric charge - coulomb, abbreviated as C.
In this unit of measurement (and this is the contemporary definition of this unit) the electric charge of an electron, used as negative value, or of a proton, used as positive value, is

Therefore, 1 Coulomb is approximately equal to the amount of electricity in / (1.602176634·10−19) electrons.
The word "approximately" is used because the above quantity must be an integer (since we are talking about the number of electrons), which it is not. So, the true definition of a coulomb is as stated above.

Historically, coulomb was defined differently. When electrons are moving along some conductive material, they form an electric current, which physicists have measured in amperes - units of electric current, which they have defined separately, using electromagnetic properties of a current. Knowing the electric current, they have defined 1 coulomb of electric charge as an amount of electricity, transferred by an electric current of 1 ampere during 1 second.
This different, more complicated approach to define coulomb was recently changed to a simpler one described above.

To have an understanding of the amount of electric charge of 1 coulomb, let's get back to a previous lecture that stated that the total number of electrons in one cubic centimeter of iron is 2.2·1024. Reducing the size to one cubic millimeter, it makes the number of electrons in it equal to 2.2·1021.
If each electron has a charge of 1.602176634·10−19C, as is defined above, we can calculate the total electric charge of all electrons in a cubic millimeter of iron:
2.2·1.6·1021−19C ≅ 3.5·102

So, in one cubic millimeter of electrically neutral iron we have about 350C of negative electric charge in all its electrons and 350C of positive electric charge in all its protons. Their mutual attraction hold the structure of the atoms inside. There is no excess nor deficiency of electrons, which makes the whole object electrically neutral.

Coulomb is a large unit. Getting back to an experiment with two pieces of iron presented in the previous lecture, let's reduce the size of pieces to a cubic millimeter, position them at a distance of 100 meters and magically transform all electrons from one piece to another. Then the charge of one piece will be positive +350C and the charge of another will be negative −350C.
Under these conditions the attraction force between them will be about 1.1·1011N (newtons), which is huge and is about twice the weight of a great pyramid of Giza.

As another example, the amount of electricity passing through a regular incandescent lamp of 60W is about 0.5C per second.

We present these examples without any proof, just for demonstration of the concept of amount of electricity. In the future lectures we will learn the laws of electricity and all these calculations will be presented in details.

Monday, December 23, 2019

Unizor - Physics4Teens - Electromagnetism - Carrier of Electricity

Notes to a video lecture on

Carrier of Electricity

Electricity is a form of energy.
Mechanical energy is carried by moving objects. Thermal energy is carried by oscillating molecules. Electricity, as a form of energy, must have its carrier too.

As we know, any object consists of molecules that retain the object's properties. There are thousands of different molecules, corresponding to thousands of different in their characteristics objects.

Molecules are comprised from atoms, which have completely different characteristics. There are just a little more than a hundred different atoms, from their compositions all molecules are built.

Each atom, according to a classical model that we will use when talking about electricity, consists of a nucleus, where certain number of protons and neutrons are bundled together, and electrons that rotate on different orbits around a nucleus.

What force keeps electrons on their orbits?
Similarly to gravitational force that keeps planets on their orbits around a sun, there is a force between a nucleus and electrons circling on their orbits.
This force is called electric force. As in case of gravity, we can talk about electric field as a domain of space, where electric forces are acting.

Numerous experiments show that the attracting electric force exists between protons and electrons. Neutrons do not play any role in keeping electrons on their orbits. Further experiments showed that, while protons and electrons are attracted to each other, two protons repulse each other, and so are two electrons. That prompted the designation of terms positive and negative to describe the electric energy carried, correspondingly, by protons and electrons and the term electric charge to name and quantify this form of energy.

So, we say that protons carry positive electric charge, while electrons carry negative electric charge. Positive and negative electric charges attract and neutralize each other, while two positive or two negative charges repulse each other.

In a normal state atoms have equal number of protons and electrons, thus are electrically neutral, which implies that the amount of electric charge in one proton and one electron are equal, though opposite in "sign". Obviously, our designation of "positive" and "negative" is just for a convenience of description and ease of calculations.

Under some circumstances the number of electrons in an object might be greater or less than the number of protons, which causes the entire object to be negatively (when there is an excess of electrons) or positively (when there is a deficiency of electrons) charged.

In case of excess of electrons, some electrons are no longer attached to a nucleus, but travel freely inside the object. Because of the excess of electrons, the entire object becomes negatively charged.
When there is a deficiency in number of electrons, certain spots on certain orbits around certain nuclei remain empty. The entire object becomes positively charged.
If a negatively charged object A comes to contact with a positively charged object B, excess electrons from A might migrate to B, thus diminishing negative charge of A by diminishing excess of electrons and diminishing positive charge of B by filling empty spaces on the orbits of those atoms that had deficiency of electrons.

Electric force is really strong. As an example, let us consider two small cubes of iron of 1 cm³ each positioned at the distance of 1 meter from each other.
There are 8.4·1022 atoms in each cube. Each atom contains 26 protons, 30 neutrons and 26 electrons.
If we magically strip all atoms in one cube of iron of all their electrons and transfer them to another cube, the one with deficiency of electrons will be positively charged and the one with excess electrons will be negatively charged. So, they will attract each other.
The total number of excess electrons in one cube, which is equal to the total number of deficient electrons in another one is
26·8.4·1022 ≅ 2.2·1024
The distance between them is 1 meter. According to Coulomb Law, that we will study later, the force of attraction between these two small cubes of iron will be, approximately
F = 1.11·1021 N (newtons)
Just as a comparison, the force of gravity that keeps the planet Mars on its orbit around the Sun is equal to 1.6·1021 N, which is quite comparable.
It also shows how much stronger electrical forces are, compared to gravitational.

Fortunately, we never have to deal with such strong forces, all atoms that comprise an object are never stripped of all their electrons.

It's easy to see electricity in action.
Lightning is the flow of electrons from the negatively charged cloud to some object on the ground.
Getting off some synthetic clothes is accompanied by small visible in the dark and audible sparks, which are also the flows of electrons from an object with excess of electrons to an object with their deficiency.

An electroscope is a device that can demonstrate the excess or deficiency of electrons, that is whether an object is electrically charged.

Initially, the electroscope is electrically neutral and aluminum foils are in vertical position, as there is no electrical force between them.
If electrically charged object touched the metal disc of an initially neutral electroscope, excess or deficiency of electrons in an object will be shared with metal disc and, further, with aluminum foils. This will negatively or positively charge both aluminum foils, and they will split apart because the same electrical charge (positive or negative) repulse objects (aluminum foils in this case).
With proper calibration this effect can be used to measure the amount of electricity by the angle of deviation of aluminum foils from vertical, as more electrons are in excess or deficiency - the stronger the repulsive force will be between the foils, and the greater angle of deviation of their position from the vertical will be.

Tuesday, December 3, 2019

Unizor - Physics4Teens - Energy - Light as Quants

Notes to a video lecture on

Quants of Light

By the end of 19th century the electrons, as carriers of electricity, were discovered by Sir Joseph Thomson in 1897, and many scientists experimented with electricity.

At that time the wave theory of light was dominant. It could explain most of experimental facts and was shared by most physicists.
However, there were some new interesting experimental facts that could not be easily explained in the framework of the classical wave theory of light as oscillation of electromagnetic field.

The photoelectric effect was one of such experimental facts that physicists could not fit into classical wave theory.

Consider a simple electrical experiment when two poles, positive and negative, positioned close to each other, are gradually charged. After a charge reaches certain value, a spark between these poles causes the discharge of electricity.

The electric charge was attributed to electrons with a negatively charged pole having more electrons than in an electrically neutral state and a positively charged one having less electrons than in an electrically neutral state.
The electric spark was the flow of excess electrons from a negative pole to a positive one, thus bringing them both to an electrically neutral state.

It was observed that, if the negative pole is lit by light, the discharge occurs earlier, with less amount of charge accumulated in the poles.
This was so-called photoelectric effect.

The experimental characteristics of the photoelectric effect were:
(a) if photoelectric effect is observed with specific frequency of the light, the number of electrons leaving the negative pole in a unit of time is proportional to intensity of the light;
(b) the speed of photo-electrons and, therefore, their kinetic energy do not depend on intensity of light, but on its frequency; higher intensity light produces more electrons, but their speed remains the same, while higher frequency light produces faster photo-electrons;
(c) for each material, used as a negative pole, there is minimal frequency of light necessary to initiate the photoelectric effect; high intensity or prolong time exposure to light of a lesser frequency do not produce photoelectric effect.

The explanation coming to mind within a framework of the wave theory of light would be as follows.
Light is oscillations of the electromagnetic field. Electrons, accumulated during the charging process, are vibrating more intensely as a result of the oscillations of the electromagnetic field of the light, whose energy is transformed to electrons, so photo-electrons leave the negative pole easier, thus facilitating an earlier discharge.

This would be a great explanation if not for a couple of contradictory facts.
The first contradiction is the property (b) of the photoelectric effect. According to the classical wave theory, the speed of photo-electrons must be dependent on the intensity of the light (amplitude of electromagnetic waves), which was not observed. And the (c) property is also unexplainable by classical wave theory, because, again, within a framework of the classical wave theory for any frequency we can find an intensity of light sufficient to "knock" out the electrons from the negative pole or keep the light of lesser intensity long enough time to transfer to electrons sufficient amount of energy to fly off the surface of the pole, which was not observed.

The explanation of these phenomena came with introduction of quants of light - a hypothesis offered by Planck and used by Einstein to explain the properties of photoelectric effect.

According to the explanation of photoelectric effect offered by Einstein, light propagates in space not as a continuous stream of waves of electromagnetic oscillations, but in small indivisible packets (quants of light or photons), separated in space and traveling along the same path, thus resurrecting the corpuscular theory, but without rejecting the electromagnetic origin of light.

The energy of each photon proportionally depends on the frequency of oscillation of electromagnetic field that carries the light, not on intensity of light, with intensity of light being just a measure of the number of photons passing through a point in space in a unit of time.

The energy of light is absorbed by electrons also in these photons. To break away the electron needs certain minimal energy.
If the energy of a single photon is sufficient to overcome the atomic forces that keep the electron inside the negative pole, this electron becomes a photo-electron and flies away to a positive pole.
If the energy of a photon is less than this minimal amount necessary to overcome the atomic forces, this energy is dissipated as heat, and no photo-electrons are produced.

Within the framework of this new quantum theory of light all the characteristics of the photoelectric effect can find their explanation.
Let's analyze them.

(a) If photoelectric effect is observed with specific frequency of the light, the number of electrons leaving the negative pole in a unit of time is proportional to intensity of the light;
Explanation: each photon has sufficient amount of energy to "knock" out an electron, and intensity is the number of such photons per unit of time.

(b) The speed of photo-electrons and, therefore, their kinetic energy do not depend on intensity of light, but on its frequency; higher intensity light produces more electrons, but their speed remains the same, while higher frequency light produces faster photo-electrons;
Explanation: speed of electrons and, therefore, their kinetic energy depend on the energy of a photon that "knocked" these electrons out, which, in turn, is proportional to the frequency of light, while intensity of light (the number of photons per unit of time) affects the number of photo-electrons produced by light, not their individual energy.

(c) For each material, used as a negative pole, there is minimal frequency of light necessary to initiate the photoelectric effect; high intensity or prolong time exposure to light of a lesser frequency do not produce photoelectric effect.
Explanation: the energy, needed by an electron to break away from atomic forces that keep it inside the material, obviously depend on the material; as soon as the light frequency is sufficient for one photon to carry that amount of energy, the photoelectric effect can start; photons of lesser level of frequency cannot "knock" out the electrons from the surrounding material, and the energy of the light is just dissipated as heat.