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# Electromagnetism – 1 Introduction to Electromagnetism

## Introduction

Electromagnetism is a field of “Classical physics”, which studies Electric and Magnetic phenomena in nature.

Electric (from Greek electron, Amber) phenomena were observed for the first time in 600 b.C. from Thales by Miletus, and were formalised many centuries later by James Clerk Maxwell in the 1800s.

Even if Electromagnetism is part of Classical Physics, it is compatible with Special Relativity, and Quantum mechanics requires some adjustments on electromagnetism only under certain conditions (atomic lengths, such as 0.5 Å, which is in the International System $0.5 10^{-10}m$).

## Forces

In Classical Physics, we do have two types of forces: Forces by Contact and Distance forces.

Examples of Contact Forces

• Friction Force
• Normal Reaction Force
• Elastic force

Examples of Distance Forces

• Gravitational Force
• Electromagnetic Force

Gravitational force is a distance force that people experience everyday (when the electromagnetic force was not so easy to detect in the past centuries). The main difference between the gravitational force and the electromagnetic one is the fact that if Gravitational Force can be attractive only, the Electromagnetic force can be both attractive and repulsive depending on the cases.

In gravitational force, the source of gravity attraction is a mass, which has a positive value: the force results attractive because of this positive value of the mass. At this point it should be clear that in electromagnetic force, since it can be both attractive and repulsive, the source can vary in sign.

In fact, we may have a positive or negative electric source. This electric source’s minimum value is e and every electric source is an integer multiple of e. Let’s see it more in detail.

## Charges: Electrons and Protons

Macroscopically, we can distinguish between two types of substances: Glass substances (+) and Resinous Substances (-). Rubbing them, we can see a “charge” phenomenon. The electrons, some elementary constituents of matter, are moving. When they “go away” we have a positive charge. If they accumulate, we have a negative charge.

It’s clear that electrones and negative charge do have a very strong connection (we may now wonder what’s connected with a positive charge). Rubbing these substances, we’ll make electrones accumulate or escape, resulting in a certain charge, according to the nature of the substance we’re working with.

As a source, a charge exerts a distance force, attractive or repulsive according to its sign. In fact, Electromagnetism is strongly connected to matter structure: matter is made by atoms, and these atoms constituents are the electron, the proton and the neutron.

Protons ($\rho^+$) and neutrons (n) are 1840 times more massive than the electron ($e^-$), they are bonded together to form the nucleus (that’s why they’re called nucleons).
The electron spins around the nucleus, from a distance from its centre of 0.5 Å ($0.5 10^{-10}$m).

From another perspective, now we want to analyse them and describe their electric characteristics: the electron has a negative charge $-|e| = -1.610^{-19}$C. where C is the unit of Coulombs, used to measure charges.
On the other hand, protons have a positive charge $|e| = 1.610^{-19}$C.

The Electric Charge is a property of subatomic particles that causes it to experience a force when placed in an electromagnetic field. Protons and Electrons are carriers of this charge e. In nature we may only have an integer multiple of this charge.

The simple rule is: 1 Charge carrier – 1 Charge unit.

Said that, we should now mention that neutrons are not charge carriers (since they do not have any charge, they are considered neutral).

In an atom, the number of electrons is equal to the number of protons, which is called atomic number. Different atomic numbers define different elements in nature, but it’s important to add that different neutron values in a nucleus do not affect the atomic nature of the element. In fact, a variation in neutrons will result in an isotropic variation of the same element, for example Hydrogen, which is made of one proton and one electron, when has two nucleons, a proton and an adding neutron, will present a variation of Hydrogen called Deuterium (Deuterium is one of two stable isotopes of hydrogen. The nucleus of a deuterium atom, called a deuteron, contains one proton and one neutron, whereas the far more common protium has no neutrons in the nucleus). Keep in mind that stable isotopes are not so common (for example, on Earth Deuterium is 0,0156% of total Hydrogen, and 98% of matter in the universe is made by Hydrogen and Helium).

Let’s make it more clear with a table, considering some stable isotopes.

Element Isotropic Protons Neutrons
Hydrogen - 1 0
Hydrogen Deuterium (rare) Hydrogen 1 1
Hydrogen Tritium (rare) Hydrogen 1 2
Helium - 2 0
Helium-3 (very rare) Helium 2 1
Helium-4 (common ) Helium 2 4

## Conductors and Insulators

The movement of electrons is called “electric current”. Some materials allow electrons to freely flow through it, whereas insulators don’t allow it. This happens because conductors atoms (such as gold, silver, copper) do have 1-2 electrons free-to-move, since they are very weakly bonded to the atom. A very small amount of energy will make them move away and freely flow.

It’s easy to understand that in the insulator case, the electrons are strongly bound, and everything is stuck since the electrons are not able to freely-move: they can jump around in their own atom or be shared with the closest atom.

We need to keep in mind this: in insulators we may have a localised charge and the electric current is not allowed. In Conductors we have a free river of electrons. These differences will be important to solve some electrostatic problems, where we’ll need to understand how to handle the different cases.

## Electric contact and Electric induction

A is a conductor, positively charged (7e) and B is a neutral conductor (neutral means, the total charge is zero, let’s say 4e-4e). By contact the electrons are attracted from B to A. It’s important to keep in mind that if one conductor is charged and the second one is neutral and they are two equal conductors, the charge distribution will be equal.

A similar phenomenon occurs without contact, when one of the conductors is “grounded”, which means connected to another Giant conductor (like the earth, that’s why grounded).

A charged conductor C’, which is positively charged, is approaching C, which is neutral. They’re both on an insulator, so the charges liberally flow only in the conductors. When C’ is close to C, the electrons in C are attracted by its positive charge, so they will move in C’ direction, without leaving C (they are trapped in C, since there is no contact).
Connecting C to the ground (you should consider Earth as a giant conductor), the positive charges in C will leave, thanks to the repulsive force. At this point, disconnecting C from the ground will make C negatively charged. ## Columbian force

Charges can be measured with a Gold Leaf electroscope, this experiment explains how. Two golden leafs are free to move from their starting position, rotating by an angle .

Touching the Conductive Plate (which is connected to the gold foil leaves) with a Conductive Rod the charges will have an equal distribution on the leaves resulting in their rotation relative to the y-axis in the middle of them, because of repulsive electromagnetic force.

We already said that the Electromagnetic Force is a distance force: the electric force generated by a charge source is called Columbian Force, because of Coulomb (Charles-Augustin de Coulomb, discoverer of the description of the electrostatic force of attraction and repulsion. The SI unit of charge has been named Coulomb in his honour).

Since Gravitational force and electrostatic force seemed to be similar, Coulomb had the idea to use a torsion balance (very similar to Cavendish Balance) to find an operative description of this new force. Hence he found:

$F = k \frac{|q_1 q_2|}{r^2} \hat{r}$ with $k = \frac{1}{4\pi\epsilon_{0}}$

and $\epsilon_{0} = 8.8541878128 \times 10^{-12} \, F \cdot m^{-1}$