Electric charge and Coulomb's law.

Charge

• there are two kinds of charge, positive and negative
• like charges repel, unlike charges attract
• positive charge comes from having more protons than electrons; negative charge comes from having more electrons than protons
• charge is quantized, meaning that charge comes in integer multiples of the elementary charge e
• charge is conserved

Probably everyone is familiar with the first three concepts, but what does it mean for charge to be quantized? Charge comes in multiples of an indivisible unit of charge, represented by the letter e. In other words, charge comes in multiples of the charge on the electron or the proton. These things have the same size charge, but the sign is different. A proton has a charge of +e, while an electron has a charge of -e.
Electrons and protons are not the only things that carry charge. Other particles (positrons, for example) also carry charge in multiples of the electronic charge. Those are not going to be discussed, for the most part, in this course, however.
Putting "charge is quantized" in terms of an equation, we say:
q = n e
q is the symbol used to represent charge, while n is a positive or negative integer, and e is the electronic charge, 1.60 x 10^-19 Coulombs.

The Law of Conservation of Charge

The Law of conservation of charge states that the net charge of an isolated system remains constant.
If a system starts out with an equal number of positive and negative charges, thereıs nothing we can do to create an excess of one kind of charge in that system unless we bring in charge from outside the system (or remove some charge from the system). Likewise, if something starts out with a certain net charge, say +100 e, it will always have +100 e unless it is allowed to interact with something external to it.
Charge can be created and destroyed, but only in positive-negative pairs.
Table of elementary particle masses and charges:

Electrostatic charging

Forces between two electrically-charged objects can be extremely large. Most things are electrically neutral; they have equal amounts of positive and negative charge. If this wasnıt the case, the world we live in would be a much stranger place. We also have a lot of control over how things get charged. This is because we can choose the appropriate material to use in a given situation.
Metals are good conductors of electric charge, while plastics, wood, and rubber are not. Theyıre called insulators. Charge does not flow nearly as easily through insulators as it does through conductors, which is why wires you plug into a wall socket are covered with a protective rubber coating. Charge flows along the wire, but not through the coating to you.
Materials are divided into three categories, depending on how easily they will allow charge (i.e., electrons) to flow along them. These are:

• conductors - metals, for example
• semi-conductors - silicon is a good example
• insulators - rubber, wood, plastic for example

Most materials are either conductors or insulators. The difference between them is that in conductors, the outermost electrons in the atoms are so loosely bound to their atoms that theyıre free to travel around. In insulators, on the other hand, the electrons are much more tightly bound to the atoms, and are not free to flow. Semi-conductors are a very useful intermediate class, not as conductive as metals but considerably more conductive than insulators. By adding certain impurities to semi-conductors in the appropriate concentrations the conductivity can be well-controlled.
There are three ways that objects can be given a net charge. These are:

1. Charging by friction - this is useful for charging insulators. If you rub one material with another (say, a plastic ruler with a piece of paper towel), electrons have a tendency to be transferred from one material to the other. For example, rubbing glass with silk or saran wrap generally leaves the glass with a positive charge; rubbing PVC rod with fur generally gives the rod a negative charge.
   
2. Charging by conduction - useful for charging metals and other conductors. If a charged object touches a conductor, some charge will be transferred between the object and the conductor, charging the conductor with the same sign as the charge on the object.
   
3. Charging by induction - also useful for charging metals and other conductors. Again, a charged object is used, but this time it is only brought close to the conductor, and does not touch it. If the conductor is connected to ground (ground is basically anything neutral that can give up electrons to, or take electrons from, an object), electrons will either flow on to it or away from it. When the ground connection is removed , the conductor will have a charge opposite in sign to that of the charged object.

An example of induction using a negatively charged object and an initially-uncharged conductor (for example, a metal ball on a plastic handle).
(1) bring the negatively-charged object close to, but not touching, the conductor. Electrons on the conductor will be repelled from the area nearest the charged object.
(2) connect the conductor to ground. The electrons on the conductor want to get as far away from the negatively-charged object as possible, so some of them flow to ground.
(3) remove the ground connection. This leaves the conductor with a deficit of electrons.
(4) remove the charged object. The conductor is now positively charged.
A practical application involving the transfer of charge is in how laser printers and photocopiers work.

Why is static electricity more apparent in winter?

You notice static electricity much more in winter (with clothes in a dryer, or taking a sweater off, or getting a shock when you touch something after walking on carpet) than in summer because the air is much drier in winter than summer. Dry air is a relatively good electrical insulator, so if something is charged the charge tends to stay. In more humid conditions, such as you find on a typical summer day, water molecules, which are polarized, can quickly remove charge from a charged object.

Try this at home

See if you can charge something at home using friction. I got good results by rubbing a Bic pen with a piece of paper towel. To test the charge, you can use a narrow stream of water from a faucet; if the object attracts the stream when it's brought close, you know it's charged. All you need to do is to find something to rub - try anything made out of hard plastic or rubber. You also need to find something to rub the object with - potential candidates are things like paper towel, wool, silk, and saran wrap or other plastic.

Coulomb's law

The force exerted by one charge q on another charge Q is given by Coulomb's law:

r is the distance between the charges.
Remember that force is a vector, so when more than one charge exerts a force on another charge, the net force on that charge is the vector sum of the individual forces. Remember, too, that charges of the same sign exert repulsive forces on one another, while charges of opposite sign attract.

An example

Four charges are arranged in a square with sides of length 2.5 cm. The two charges in the top right and bottom left corners are +3.0 x 10^-6 C. The charges in the other two corners are -3.0 x 10^-6 C. What is the net force exerted on the charge in the top right corner by the other three charges?

To solve any problem like this, the simplest thing to do is to draw a good diagram showing the forces acting on the charge. You should also let your diagram handle your signs for you. Force is a vector, and any time you have a minus sign associated with a vector all it does is tell you about the direction of the vector. If you have the arrows giving you the direction on your diagram, you can just drop any signs that come out of the equation for Coulomb's law.
Consider the forces exerted on the charge in the top right by the other three:

You have to be very careful to add these forces as vectors to get the net force. In this problem we can take advantage of the symmetry, and combine the forces from charges 2 and 4 into a force along the diagonal (opposite to the force from charge 3) of magnitude 183.1 N. When this is combined with the 64.7 N force in the opposite direction, the result is a net force of 118 N pointing along the diagonal of the square.

The symmetry here makes things a little easier. If it wasn't so symmetric, all you'd have to do is split the vectors up in to x and y components, add them to find the x and y components of the net force, and then calculate the magnitude and direction of the net force from the components. Example 16-4 in the textbook shows this process.

The parallel between gravity and electrostatics

An electric field describes how an electric charge affects the region around it. It's a powerful concept, because it allows you to determine ahead of time how a charge will be affected if it is brought into the region. Many people have trouble with the concept of a field, though, because it's something that's hard to get a real feel for. The fact is, though, that you're already familiar with a field. We've talked about gravity, and we've even used a gravitational field; we just didn't call it a field.
When talking about gravity, we got into the (probably bad) habit of calling g "the acceleration due to gravity". It's more accurate to call g the gravitational field produced by the Earth at the surface of the Earth. If you understand gravity you can understand electric forces and fields because the equations that govern both have the same form.
The gravitational force between two masses (m and M) separated by a distance r is given by Newton's law of universal gravitation:

A similar equation applies to the force between two charges (q and Q) separated by a distance r:

The force equations are similar, so the behavior of interacting masses is similar to that of interacting charges, and similar analysis methods can be used. The main difference is that gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive. The charge (q or Q) plays the same role in the electrostatic case that the mass (m or M) plays in the case of the gravity.
A good example of a question involving two interacting masses is a projectile motion problem, where there is one mass m, the projectile, interacting with a much larger mass M, the Earth. If we throw the projectile (at some random launch angle) off a 40-meter-high cliff, the force on the projectile is given by:
F = mg
This is the same equation as the more complicated equation above, with G, M, and the radius of the Earth, squared, incorporated into g, the gravitational field.
So, you've seen a field before, in the form of g. Electric fields operate in a similar way. An equivalent electrostatics problem is to launch a charge q (again, at some random angle) into a uniform electric field E, as we did for m in the Earth's gravitational field g. The force on the charge is given by F = qE, the same way the force on the mass m is given by F = mg.
We can extend the parallel between gravity and electrostatics to energy, but we'll deal with that later. The bottom line is that if you can do projectile motion questions using gravity, you should be able to do them using electrostatics. In some cases, youıll need to apply both; in other cases one force will be so much larger than the other that you can ignore one (generally if you can ignore one, it'll be the gravitational force).

Explanation of Coulomb's Law.

Explanation of Coulomb's Law: Electrically Charged Objects. Also, Historical Quote.

The French engineer Charles Coulomb investigated the quantitative relation of forces between charged objects during the 1780's. Using a torsion balance device, created by Coulomb himself, he could determine how an electric force varies as a function of the magnitude of the charges and the distance between them.
Coulomb used little spheres with different charges whose exact value he did not know, but the experiment allowed him to test the relation between the charges. Coulomb realized that if a charged sphere touches another identical not charged sphere, the charge will be shared in equal parts symmetrically. Thus, he had the way to generate charges equal to ½, ¼, etc., from the original charge. Keeping the distance constant between the charges he noticed that if the charge of one of the spheres was duplicated, the force was also duplicated; and if the charge in both spheres was duplicated, the force was increased to four times its original value. When he varied the distance between the charges, he found the force decreased in relation to the square of the distance; that is, if the distance was duplicated, the force decreased to the fourth part of the original value.
In that way Coulomb demonstrated that the electric force between two stationary charged particles is :
- Inversely proportional to the square of the distance r between the particles and is directed along the line that joins them.
- Proportional to the product of the charges q₁ and q₂.
- Attracted if the charges have opposite electrical sign and repulsed if the charges have equal sign.
Coulomb 's Law can be expressed in the form of an equation :

The validity of Coulomb's Law has been verified with modern devices that have detected that the exponent 2 has an exactitude of one part in 10¹⁶.

K_e is a constant known as the Coulomb 's constant, which in the International System units has the value K_e = 8.987x10⁹ Nm²/C².

The International System unit for charge is the Coulomb.
The smallest known charge in nature is the charge of an electron or proton, which has an absolute value of e = 1.60219x10^-19 C.
Thus, a 1 Coulomb charge is approximately equal to a charge of 6.24x10¹⁸ (= 1C/e) electrons or protons.
We should notice that the force is a vectorial quantity, that is, has magnitude and direction. Coulomb 's Law expressed in vectorial form for the electric force F₁₂ exerted by a charge q₁ over a second charge q₂ is (bold type is used to denote vectorial quantities):



As every force obeys Newton's third Law, the electric force exerted by q₂ over q₁ is equal in magnitude to the force exerted by q₁ over q₂ and in the opposite direction, that is F₂₁= - F₁₂.
If q₁ and q₂ have the same sign, F₁₂ takes the direction of r. If q₁ and q₂ have opposite sign, the product q₁q₂ is negative and F₁₂ points opposite to r.
When two or more charges are present, the force between any pair of them is given by the above equation. Hence, the resultant force on any of them is equal to the vectorial sum of the forces exerted by the different individual charges

. For example, with three charges, the resultant force exerted by particles 2 and 3 over 1 is

F₁ = F₂₁ + F₃₁

Einstein Childhood.

was slow in learning how to speak. His parents even consulted a doctor. He also had a cheeky rebelliousness toward authority, which led one headmaster to expel him and another to amuse history by saying that he would never amount to much. But these traits helped make him a genius. His cocky contempt for authority led him to question conventional wisdom. His slow verbal development made him curious about ordinary things – such as space and time – that most adults take for granted. His father gave him a compass at age five, and he puzzled over the nature of a magnetic field for the rest of his life. And he tended to think in pictures rather than words.When Einstein was born, his mother worried that his head was too large and his grandmother exclaimed that he was "much too fat." A few years later, when Einstein was four or five, he had his first scientific experience: his father showed him a pocket compass and the young boy marveled at the fact that regardless of where the compass was turned, the needle always pointed north. The needle's invariable northward swing, guided by an invisible force, profoundly impressed the child. The compass convinced him that there had to be "something behind things, something deeply hidden."
Einstein's formal education began at age six, when he enrolled in the Petersschule on Blumen- strasse, a Catholic elementary school in Munich. Since his parents were not practicing Jews, they cared more about the school's academic standards than its religious affiliation. Einstein did well in school, but he was a quiet child and kept his distance from his peers. He was uncomfortable with the principle of absolute obedience and the military drills that dominated the school's atmosphere.
Even as a small boy Albert Einstein was self-sufficient and thoughtful, and demonstrated an interest in science and problem-solving even before he entered school. According to family legend he was a slow talker, pausing to consider what he would say. His sister remembered the concentration and perseverance with which the young Einstein preferred to build houses of cards and play with his sister at home.At the age of ten, Einstein was accepted into the Luitpold Gymnasium in Munich, a formal and respected institution that emphasized Latin and Greek over mathematics and science. Unhappy with the educational program at school, Einstein turned to a course of personal study outside of school. His Uncle Jakob lent him a book of algebra and sent him math puzzles to solve. In addition, a friend of Einstein's family, lent him books on popular science and philosophy that the young boy eagerly devoured.

On November 18 in 1881 Albert Einstein’s (1879–1955) sister Maria – called Maja – was born in Munich. Her Jewish parents, Hermann Einstein and Pauline Einstein, nee Koch, had moved from Ulm to Munich in June 1880 with their two-year-old son Albert. There Hermann Einstein and his brother Jakob had founded the electrical engineering company Einstein & Cie. When little Albert saw his sister for the first time he thought she were a kind of toy and asked: “Yes, but where does it have its small wheels?” Maja and her brother Albert got along very well all their life.

After attending the elementary school in Munich from 1887 to 1894, she attended the German International School in Milan where the family had moved to due to financial reasons. To complete school, Albert had stayed in Munich. From 1899 to 1902 she attended the workshop for teachers in Aarau. After she did her final exams successfully, she studied Romance languages and literature in Berlin, Bern and Paris. In 1909 she graduated from university in Bern. The title of her dissertation was “Contribution to the tradition of the Chevalier au Cygne and the Enfances Godefroi”. In the following year the “Ms Doctor” married Paul Winteler. Their marriage produced no children. Albert Einstein had lived with the family Winteler during his almost one year long stay in Aarau (1895/96).

The young couple moved to Luzern in 1911 where Maja’s husband had found a job. In 1922 they moved to Colonnata near Florence in Italy.

Due to the political difficulties in Europe Maja, she was Jewish, emigrated, to the United States in 1939. As her husband wasn’t allowed to enter the United States due to health reasons he stayed with relatives in Geneva. He died in 1952. Maja moved to her brother into Mercer Street in Princeton, New Jersey. Albert Einstein’s second wife Elsa had died there in 1936. The siblings spent some nice years together. After a stroke in 1946 and later through a proceeding arteriosclerosis Maja was bedridden.