# P. Rule . The 'Coulomb' is the SI unit for Electric Charge. Specifically, it is defined as the "amount of electric charge transported by a current of one ampere flowing for one second" (see definitions of each new term, they are gone over in more depth later on).

By itself, a Coulomb is a huge amount of charge - charged particles like protons and electrons have electric charges many orders of magnitude smaller than a single Coulomb. Two objects, each with one Coulomb of charge, located one meter apart, experience an electric force (see Subsection XII.III) of roughly nine billion Newtons.

# P. Rule . An atom is the smallest unit of matter retaining the chemical properties of its element. It is composed of a dense nucleus with Protons and Neutrons, and surrounded by orbitals of Electrons.

Electrons & Protons are small particles (e.g., specks of mass) that carry an electric charge with a magnitude of ~1.602 × 10⁻¹⁹ Coulombs, which is referred to as the "Elementary Charge". Protons are positively charged, while electrons are negatively charged.

Electrons are elementary particles, indivisible by nature, while protons and neutrons are composed of quarks, the REAL smallest particles. Specifically, the proton has two up quarks and one down quark.

The up quark has a charge of +(2/3)e, while the down quark has the charge -(1/3)e. Thus, the net quark of a proton is +e.

The neutron, being composed of one up quark and two down quarks, has a net charge of 0. If this were not the case, the neutron would not be electrically neutral, and the nucleus of an atom would tear apart as the protons would repel from one another without the stabilizing force of the neutrons.

The electron, being an elementary particle (defined below), just has a net charge of -e.

# P. Rule . There is an equation relating net charge and elementary charge (or any quantifiable proportion of elementary charge), useful for determining how many excess charge carriers it would take for a specific net charge to be achieved:

q = n × e

q = Net charge on an object
n = Excess number of charge carriers (protons or electrons or whatever - it just has to be ONE of them).
e = The Elementary Charge Constant.

# P. Rule . Charge is quantized, meaning that it must come in discrete quantities, integer multiples of the elementary charge. This is because the 'net charge' of an object is the product of having more or fewer charged particles, and thus only multiples of the elementary charge are possible (since elementary particles are indivisible).

Using the net/elementary charge relation (see Rule 159), one can find that it is impossible for an object to have a net negative charge of 2.00 × 10⁻¹⁹ Coulombs, as such a net force would require 1.25 electrons, violating quantization.

# P. Rule . When the atoms of a conductor form a solid, some of their outermost (and most loosely held) electrons become free to wander about within the solid, leaving behind positively charged atoms (positive ions). These wandering electrons are known as conduction electrons. There are practically no free electrons in a nonconductor, since those electrons are tightly bound to their atoms.

Knowledge of the "mobility of charge" within conductors, and conductors alone, is fundamental for comprehending concepts in Electric Field and Charge-Flux Law type questions - see Rule [[[. [[[this will be the bottom notepad Rule]]]

# P. Rule . Law of Electric Force (Coulomb's Law): VECTOR.

Units: Newtons.


Equation:

F_e = (k × q₁ × q₂) / (r²)

F_e = The magnitude of the electric force that exists between two charged particles.
k = The Coulomb constant, equal to 8.99 × 10⁹ (N × m²) / (C²).
q₁ = The net charge on object 1, measured in Coulombs.
q₂ = The net charge on object 2, measured in Coulombs.
r = The distance between the centers of charge of the two objects.


Definition: Coulomb's Law, hereafter referred to as the Law of Electric Force, enables one to find the magnitude of the Electric Force with respect to two particles.

Note that this equation looks very similar to the Universal Law of Gravitation (see Rule 142). Accordingly, k (the Coulomb constant) functions similar to G (the Gravitational constant), being equal to (N × m²) / (a particular composition property of mass)². Clearly, since the Coulomb constant is 20 orders of magnitude stronger than the Gravitational constant, the Electric Force between objects is much more powerful than their Gravitational attraction. F_e >>> F_g.

If the calculated Electric Force has a Negative Value, then it is an attractive force. If the Electric Force has a Positive Value, then it is a repulsive force. This is quite obvious upon momentary consideration - a negative and a positive charge will always produce a negative, and thus attractive force, which matches the Law of Charges that opposite's attract. Thus also follows for repulsive like charges.

# P. Rule . With charges, the fundamental concept to understand in applying the Law of Electric Force is that in order to derive any useful information (depending on the question, but in general), you must determine the effect of the electric force on the individual point charges. Specifically, you must be able to determine the direction the charges will move in as a result of the force.

The Law of Electric Force determines the repulsive or attractive force acting on both charges, since they're a Newton's Law Force Pair (see Rule 76). However, in addition, you must utilize this information to determine the direction of the movement of each charge. If you have a proton on the left and an electron on the right, the proton will move rightward and the electron leftward as they attract toward one another. If you have two electrons, they will move in opposite directions away from one another.

# P. Rule . Permittivity of Free Space:

The Coulomb Constant, 'k', 8.99 × 10⁹ (N × m²) / (C²), used in such equations as the Law of Electric Force (see Rule 162) and all its applications, has a special fixed relationship with another constant. This other constant is the permittivity constant, also just known as the permittivity of free space.

It is represented as ε₀ ("Epsilon Naught"), and is defined using the following relation:

(1 / 4πε₀) = k

ε₀ = The Permittivity of Free Space, equal to 8.85 × 10⁻¹² (C²) / (N × m²).
k = The Coulomb constant, equal to 8.99 × 10⁹ (N × m²) / (C²).

This, of course, can be substituted in for 'k' in any applicable equation. Furthermore, ε₀ itself appears in several equations by itself, most notably the Charge-Flux Law (see Rule 187). The reasons for the usage of Coulomb's Constant at all is a matter of historical decisioning.

The actual meaning of this 'permittivity of free space' value, is that it measures how dense an electric field, in relation to an electric charge, will be "permitted" to form.

# P. Rule . Conservation of Charge:

The total electric charge of an isolated system never changes.

q_{i total} = q_{f total}

If the conductors being touched in a conservation of charge-type equation are identical (in all manners other than charge), then the excess charge will be evenly distributed between the two conductors. For example, if there are two conductors, one with a charge of -3 nC and the other with +6 nC, then the final charge of each conductor, once touched, will be 1.5 nC.

# P. Rule . GROUND.

All excess charges can quickly be diffused through the usage of a Ground. A Ground is any sort of release point (if excess negative) or gain point (if excess positive) for the excess charges of a system: an ideal ground is an infinite well (see VII.VI) of charge carriers - such a requirement is effectively met by the Earth.

An Earth Ground is created when a circuit has a physical connection to the earth, in order to sink (lose) or source (obtain) electrons through the earth itself. The Earth has a practically infinite number of electrons that can be used to balance out a circuit/system, pulling from or giving to it. Relative to very small charged systems, the human skin could serve as a ground as well.

The end result of a ground is an electrically neutral system.

In electrical engineering, all circuits require a Ground to function - it is often referred to as "GND", and has its own symbol for use in diagrams (see E.E. Rule [[[). In many electrical situations, without the availability of a physical connection to the Earth, a "Floating Ground" can be used, which simply serves as a type of '0V reference line' (see def. of Voltage) that acts as a return path for current back to the negative side of the power supply.

# P. Rule . There are two distinct categories, processes under which charge is transferred. Specific means of transfer, like charging by friction (rubbing) fall under these wider processes. These processes are Conduction, and Induction.

Conduction:

This is the transfer of charge in which current flows because of the electric field. There are only two requisites for an object to be charged by conduction, through another object:

1. The objects have to touch.

2. The objects must, after touching, have the same sign of net charge.


Induction:

This is the transfer of charge in which a changing magnetic field generates an electromotive force (see Rule [[[), resulting in an induced charge. It is not important to fully understand what an "electromotive force" is right now, just that it is the electric force that drives current through a circuit.

There are only two requisites for an object to be charged by conduction, and they are the eact opposite of conduction:

1. The objects do not touch.

2. The objects must finish with opposite signs of net charge.

# P. Rule . Polarization:

Polarization is the process through which the charges within objects (and thus their associated particles) align themselves in such a way that there becomes a net attractive force, as a result of attraction & repulsion from an object with excess charge.

Polarization doesn't change the net charge of the object, but rather has to do with how charges rearrange themselves within the object.

The process itself is simple: When an object with an excess charge approaches a neutral object, the like charges will repel and the opposite charges will attract (the electrons being the sole moving particles, moving either in front of or behind the protons). Since the opposite charges will be closer to the charges of the object than the like charges, by the Law of Electric Force, there will be a net attractive electric force, since the opposite charges have a smaller 'r' value than the like charges.

This is the reason that balloons stick to walls once they have an excess negative charge. The wall, as an insulator without free electrons, cannot "attract" the charge of the balloon. Instead, the charges in the wall rearrange themselves and end up with that net attractive force.

Electric force due to polarization is small - objects with small masses, like balloons and aluminum cans, can be held in place and rolled respectively using only a small electric force.

Electric force caused by the polarization of a conductor is typically larger than a polarized insulator. This is because electrons in insulators are bound in their atoms, while electrons in conductors are able to move to the opposite side of the object.

# P. Rule . Placement of Charge within Conductors & Nonconductors:

The nature & positioning of the charge within the thickness of an object (like a shell or thick cylinder) differs depending on whether the material of the object is a conductor or insulator; there is no other possibility.

Conductive objects (enclosed shapes) spread out all excess charge (read: electrons) over their external surface. This is because the conduction electrons of the conductor (see Rule 161) and the excess charge electrons will repel from one another, causing the excess charge electrons to spread over and uniformly distribute across the farthest possible surface.

!!!NOTE!!!: Unless the conductor is spherical, the charge will not distribute itself uniformly. This is a matter of symmetricality, an attribute that leads spheres (shell or solid) to naturally become uniformly distributed in charge, but not for any other shape. This is not to say that a question will not simply say "assume a uniform charge density" for some ridiculous, nonspherical shape, violating the laws of physics for the sake of examining the physicist. In such a case, you would do as told and use the given information appropriately. The surface charge density σ (charge per unit area) varies over the surface of any nonspherical conductor. The electric field (see Section XIII) immediately outside of the surface of the nonspherical shape can be determined quite easily however, as described in Rule 195.

This concentration of charge on the external surface is the same for both positive and negative excess charge. If there is an excess positive charge (imagine the conduction electrons have been removed), then the positive charge will then spread uniformly across the surface.

In the state of uniform charge distribution, the conductor will be in a state of electrostatic equilibrium - see Rule [[[ for a complete explanation involving Electric Fields.

Nonconductive/Insulating objects (enclosed shapes), which do not allow free movement of charge, bind electrons to their atoms and thus do not move to redistribute excess charge. When an excess charge is added, there are conduction electrons that would even allow for the charge to be moved, and so the excess charge will simply remain wherever it is placed.

Thus, the excess charge can be uniformly distributed if that is the state in which it is added, and questions oftentime instruct the physicist to assume such a condition. However, if the charge is concentrated in a particular region, it will not naturally redistribute itself as it would in a conductor.

For a continuation of this Rule, with respect to how the conductor/nonconductor dispersal of charge affects electric field distribution, see Rule 193.

# P. Rule . Shell Theorems of Electric Force:

Shells, spherical entities of a specified thickness and a hollow interior (like a ring rotated 180° along the x-axis), retain the same importance they had in Mechanics for Electromagnetism.

Akin to the Shell Theorem for Internal Gravitation (see Rule 151), there are TWO Shell Theorems for Electric Fields - yet another similarity between electric force and gravitational force (see Rule 162 for the first). They are relatively straightforward, but are only applicable under the specified conditions.

These theorems literally do not work for any shape other than a shell/sphere - there is a particular symmetry with those specific shapes that allow these theorems to be used. They are not true for just any irregular, wack shape.

Fundamental to the understanding of these theorems is the nature of charge distribution on shells, which itself depends on whether the shell is conductive or not. See Rule 169 for a full, generalized treatment of these principles. Nonconductive shells are not in a state of electrostatic equilibrium (see Rule [[[), unlike Conductive shells.

1. A charged particle outside of a shell with charge uniformly distributed on its surface (e.g., a conductor) is attracted or repelled as if the shell’s charge were concentrated as a particle at its center. This is assuming the charge on the shell is much greater than the charge of the particle, thus not interfering with the distribution of charge on the shell (an issue detailed in Rule 169).



2. A charged particle inside a shell with charge uniformly distributed on its surface (e.g., any conductor, and any nonconstructor created in such a way) will have no net force acting on it due to the shell.

These theorems can be definitively proven using the futurely-explained Charge-Flux Theorem, done in Rule 196.