These are my complete notes for Law of Electric Force in Electromagnetism.
I color-coded my notes according to their meaning - for a complete reference for each type of note, see here (also available in the sidebar). All of the knowledge present in these notes has been filtered through my personal explanations for them, the result of my attempts to understand and study them from my classes and online courses. In the unlikely event there are any egregious errors, contact me at jdlacabe@gmail.com.
Summary of Law of Electric Force (Electromagnetism)
Table Of Contents
XII. Law of Electric Force.
XII.I Electric Charge.
The character 'q' is used to denote the net charge on an object.
#
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 section XII.II) of roughly nine billion newtons.
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 section XII.II) of roughly nine billion newtons.
# Elementary Particle: A particle that cannot be divided into smaller entities - it is a base, undivisible unit of matter. Examples include electrons, photons, and quarks.
#
P. Rule .
An atom, the smallest unit of matter retaining the chemical properties of its element, 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 ~1.69 × 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 are composed of quarks - specifically, two up quarks and one down quark.
The up quark has a charge of +(2/3)e, while the down quark has a charge of -(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 nucleus of an atom would repel
The electron, being an elementary particle, just has a net charge of -e.
Electrons are elementary particles, indivisible by nature, while protons are composed of quarks - specifically, two up quarks and one down quark.
The up quark has a charge of +(2/3)e, while the down quark has a charge of -(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 nucleus of an atom would repel
The electron, being an elementary particle, just has a net charge of -e.
# Elementary Charge: An electrical charge of 1.69 × 10⁻¹⁹ Coulombs, the standard charge of Protons and Electrons and the smallest charge recorded on an isolated particle (quarks aren't isolated). Represented as 'e'.
# MElectron (Electron Mass): 9.11 × 10⁻³¹ kg.
# MProton (Proton Mass): 1.67 × 10⁻²⁷ kg. This is over 1800x greater than the mass of an electron.
# Excess Charge: The state of an object being more negatively or positively charged due to a lack or oversupply of negatively-charged electrons, the movement of which can be facilitated by rubbing objects together (charging by friction). An "excess positive charge" is slang for an electron deficit, while an "excess negative charge" means an oversupply of electrons.
# Law of Charges:
Opposite charges attract, while like charges repel.
Example: Rubbing a balloon against one's hair will cause the electrons to move from the hair to the balloon (a transfer faciliated by rubbing), causing the balloon to stick to the hair. Furthermore, since each hair will become more positively-charged, they will repel one another, causing one's hair to stick up and separate.
#
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 = Elementary Charge
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 = Elementary Charge
#
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.
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.
XII.II Electric Force.
#
P. Rule .
Law of Electric Force (Coulomb's Law): VECTOR.
Units: Newtons.
Equation:
Fe = (k × q1 × q2) / (r²)
Fe = 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, the force produced by the Electric Charge inherent to all matter.
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. Fe >>> Fg.
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.
Units: Newtons.
Equation:
Fe = (k × q1 × q2) / (r²)
Fe = 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, the force produced by the Electric Charge inherent to all matter.
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. Fe >>> Fg.
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.
# Attractive Force: A force that pulls entities together, whether masses or charges.
# Repulsive Force: A force that pushes entities apart.
# Point Charge: An object with zero size (an infinitely small dot) that carries an electric charge. This can be generalized to any object whose mass is negligible compared to its charge. It is the Electric equivalent to a 'point mass', in that a particular charge is concentrated upon a single particle/point in space for the purpose demonstrating physical properties.
# MicroCoulombs (μC): One one millionth of a Coulomb. E.g., 1 × 10⁻⁶ C. Occasionally misstated as "Myu Coulombs", "Myu-Coulombs", etc.
# NanoCoulombs (nC): One one billionth of a Coulomb. E.g., 1 × 10⁻⁹ C.
# PicoCoulombs (pC): One one trillionth of a Coulomb. E.g., 1 × 10⁻¹² C.
#
A. 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.
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.
# Electroscope: An instrument for demonstrating electric charge. They take several forms, but generally have some place where an isolated charge (protected by some insulator, like glass) is held.
# Electricity: The flow of electrons through a conductor.
# Conductor: Something that can conduct electricity, like a wire. On the outside of a wire, there is rubber or plastic that serves as an insulator: something that doesn't conduct electricity very well or at all.
# Semiconductor: A material that holds both qualities of a conductor and insulator and can be tailored to be a better conductor or insulator. Depending on electrical signals, it can be conducting or insulating.
# Superconductor: An idealized perfect conductor, allowing charge to move without any hindrance.
#
A. 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 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.
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 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.
#
A. 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.
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.
#
A. 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.
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.
# Isolated System: A system is isolated when charges are not able to enter nor exit the system. The universe, being isolated, has a constant net charge.
#
A. Rule .
Conservation of Charge:
The total electric charge of an isolated system never changes. Emphasis on 'isolated'.
qi total = qf 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 of +6 nC, then the final charge of the conductors, once touched, will be 1.5 nC for both.
The total electric charge of an isolated system never changes. Emphasis on 'isolated'.
qi total = qf 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 of +6 nC, then the final charge of the conductors, once touched, will be 1.5 nC for both.
