Conductors - Revision history

Jbuzz at 02:22, 21 November 2025

2025-11-21T02:22:14Z

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	Created by '''David Nam Spring 2025''', ~~Claimed/~~Edited by '''Jacob Buzzard Fall 2025'''		Created by '''David Nam Spring 2025''', Edited by '''Jacob Buzzard Fall 2025'''

	==The Main Idea==		==The Main Idea==

Jbuzz at 23:27, 12 November 2025

2025-11-12T23:27:41Z

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	==History==		==History==

			===Ancient & Early Observations===
			Around 600 BC, Thales of Miletus noted that pieces of amber, when rubbed with fur, would attract lighter objects like straw or dust. This is one of the earliest recorded observations of '''static electricity''', although the concept of "conduction" was not yet defined.

			Over the following centuries, scientists and researchers noticed that certain materials allowed charge to move or discharge easily, while others seemed to hold charge with little movement. This was again before the distinction of conductors and insulators was fully developed, yet an important intuition.

			===Electricity and Conductors===
	Modern research on electricity and conductors starts in the 1700s. Many different scientists contributed to the research that led to the understanding and use of conductors. Stephan Gray was one of the first of these, first studying the idea of electricity and then conductors. In Gray's time, the general consensus was that "electric virtue" was a quality that some materials could attain and others could not. Some materials, like glass, could acquire electric virtue by friction, while others, like metal, could be given electric virtue by contact with a charged object. Gray tested this theory with many different types of material, even with a child(who did work as a conductor).		Modern research on electricity and conductors starts in the 1700s. Many different scientists contributed to the research that led to the understanding and use of conductors. Stephan Gray was one of the first of these, first studying the idea of electricity and then conductors. In Gray's time, the general consensus was that "electric virtue" was a quality that some materials could attain and others could not. Some materials, like glass, could acquire electric virtue by friction, while others, like metal, could be given electric virtue by contact with a charged object. Gray tested this theory with many different types of material, even with a child(who did work as a conductor).

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	Only when Benjamin Franklin came around some later did the ideology and vocabulary make a big switch. Franklin suggested that electricity is not created by electrical bodies through friction, but that it is a fluid shared by all bodies and can pass between them. Franklin also caused the shift in language from non-electric bodies to conductors and electric bodies to non-conductors.		Only when Benjamin Franklin came around some later did the ideology and vocabulary make a big switch. Franklin suggested that electricity is not created by electrical bodies through friction, but that it is a fluid shared by all bodies and can pass between them. Franklin also caused the shift in language from non-electric bodies to conductors and electric bodies to non-conductors.

	~~There is some evidence that ancient Egyptians~~ also used ~~electricity~~.		===Industrial & Technological Development===
			With the advent of large-scale electrical generation in the late 19th century, the need for reliable conductive materials came to the forefront of innovation. For example, copper wires began to dominate the discussion due to its superior conductivity and flexibility over iron.

			Insulation also developed: in the 1880s, the first insulated cables used gutta-percha, and later innovations included rubber and plastics such as PVC. The study of conductor materials also tied into materials science and quantum physics: understanding the "sea of electrons" model in metals, band theory, resistivity, and how different conditions affect conduction.

	~~reformat // add~~ to ~~this~~		===The Modern Era & Materials Science===
			Today, the concept of a conductor extends beyond just metals: conductive polymers, carbon-based materials, superconductors, and nanocomposites are some of the new generation of conductive materials. Now, conductors are being applied in a multitude of industries: from aerospace to biomedical to where it all started in electricity.

	== See also ==		== See also ==

Jbuzz: added more sources

2025-11-12T05:21:12Z

added more sources

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	*https://www.geeksforgeeks.org/physics/real-life-applications-of-conductors-and-insulators		*https://www.geeksforgeeks.org/physics/real-life-applications-of-conductors-and-insulators

	*		*https://histoires-de-sciences.over-blog.fr/2018/04/history-of-electricity.the-discovery-of-conductors-and-insulators-by-gray-dufay-and-franklin.html

			*https://www.copper.org/education/history/60centuries/electrical/electricity.php

			*https://www.elandcables.com/the-cable-lab/faqs/faq-what-is-the-history-of-electrical-cables


	[[Category:Which Category did you place this in?]]		[[Category:Which Category did you place this in?]]

Jbuzz: /* References */

2025-11-12T05:19:14Z

References

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	*https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499		*https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499

	*https://www.physicsclassroom.com/class/estatics/lesson-1/conductors-and-insulators~~?utm_source=chatgpt.com~~		*https://www.physicsclassroom.com/class/estatics/lesson-1/conductors-and-insulators

	*https://dadaoenergy.com/blog/what-is-an-electrical-conductor~~/?utm_source=chatgpt.com~~		*https://dadaoenergy.com/blog/what-is-an-electrical-conductor

	*https://www.geeksforgeeks.org/physics/real-life-applications-of-conductors-and-insulators~~/?utm_source=chatgpt.com~~		*https://www.geeksforgeeks.org/physics/real-life-applications-of-conductors-and-insulators

			*
	[[Category:Which Category did you place this in?]]		[[Category:Which Category did you place this in?]]

Jbuzz: added references and updated connectedness page

2025-11-12T05:15:46Z

added references and updated connectedness page

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 ==Connectedness==
-. materials science and engineering connection
-. industrial/real-life applications in electronics, power lines, and faraday cages
+===MSE (Materials Science and Engineering)===
-. polarization, charge redistribution, electric field shielding
+Conductors are extremely fundamental in materials science and engineering, since the atomic structure and behavior of electrons determine electrical properties. Materials scientists study how the arrangement of atoms, charge carrier density, lattice structure, and phonons affect conductivity and resistivity. For example:
-. nanotechnology, semiconductors, sensors, materials design
+* '''Metals:''' Copper, silver, and aluminum are excellent conductors because of their loosely bound valence electrons and nonexistent band gaps.
 ==History==
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 *https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499
 [[Category:Which Category did you place this in?]]

Jbuzz: /* History */

2025-11-12T03:46:13Z

History

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	There is some evidence that ancient Egyptians also used electricity.		There is some evidence that ancient Egyptians also used electricity.

			reformat // add to this

	== See also ==		== See also ==

Jbuzz at 03:36, 12 November 2025

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	===Simple===		===Simple===
	Material A has a ~~resitivity~~ of <math> 5.90 \cdot 10^{-8} Ω \cdot m </math> and Material B has a conductivity of <math> 1.00 \cdot 10^7 S/m </math>. They are the same size and temperature. Which is a better conductor?		Material A has a resistivity of <math> 5.90 \cdot 10^{-8} Ω \cdot m </math> and Material B has a conductivity of <math> 1.00 \cdot 10^7 S/m </math>. They are the same size and temperature. Which is a better conductor?

	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
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	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">

	We can change Material A's ~~resitivity~~ to conductivity with the formula σ = 1/ρ. σ = <math>\frac{1}{(5.90 \cdot 10^{-8} Ω \cdot m)} = 1.69 \cdot 10^7 S/m</math>. Since Material A has a greater conductivity, it is a better conductor.		We can change Material A's resistivity to conductivity with the formula σ = 1/ρ. σ = <math>\frac{1}{(5.90 \cdot 10^{-8} Ω \cdot m)} = 1.69 \cdot 10^7 S/m</math>. Since Material A has a greater conductivity, it is a better conductor.

	These numbers are the real conductivities of Zinc(Material A) and Iron(Material B).		''These numbers are the real conductivities of Zinc (Material A) and Iron (Material B).''

	</div></div>		</div></div>
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	===Difficult===		===Difficult===
	~~This should be completed by~~ a ~~student~~		A negatively charged copper sphere (conductor!) is placed near a small positively charged rod. Describe the charge distribution on the sphere and explain the resulting forces between the rod and the sphere.

	<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
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	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">

	~~solution~~		# The free electrons in the copper sphere are attracted to and move toward the positive rod, leaving a region of positive charge on the opposite side.
			# This '''induced charge separation''' creates a net attractive force between the sphere and the rod, similar to polarization problems.
			# Even though the sphere was initially neutral overall since it was a condcutor, it experiences a net force because opposite charges are closer to the rod than like charges.

			''Maybe put a harder problem here''

	</div></div>		</div></div>

	==Connectedness==		==Connectedness==
	~~#How is this topic connected to something that you are interested~~ in?		1. materials science and engineering connection
	~~#How is it connected to your major?~~		2. industrial/real-life applications in electronics, power lines, and faraday cages
	~~#Is there an interesting industrial application?~~		3. polarization, charge redistribution, electric field shielding
			4. nanotechnology, semiconductors, sensors, materials design

	==History==		==History==

Jbuzz at 03:30, 12 November 2025

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	There is a relationship between conductivity and temperature: as temperature increases, the amount of phonons, or what we can see as the vibration of atoms in the lattice, increases. This increased number of phonons scatters these freely moving electrons more frequently, increasing resistance, and therefore decreasing conductivity.		There is a relationship between conductivity and temperature: as temperature increases, the amount of phonons, or what we can see as the vibration of atoms in the lattice, increases. This increased number of phonons scatters these freely moving electrons more frequently, increasing resistance, and therefore decreasing conductivity.

	From a quantum-mechanical and materials science perspective, the behavior of conductors is governed by their energy '''band structure'''. In solids, closely spaced atomic orbitals overlap to form continuous ranges of energy that are known as bands. In '''conductors (metals)''', the '''valence band''', which contains the outer (valence) electrons and the '''conduction band''' either overlap or have a nonexistent band gap. Because of this overlap, electrons can ~~esaily~~ move to higher-energy states and flow under even a weak electric field.		From a quantum-mechanical and materials science perspective, the behavior of conductors is governed by their energy '''band structure'''. In solids, closely spaced atomic orbitals overlap to form continuous ranges of energy that are known as bands. In '''conductors (metals)''', the '''valence band''', which contains the outer (valence) electrons and the '''conduction band''' either overlap or have a nonexistent band gap. Because of this overlap, electrons can easily move to higher-energy states and flow under even a weak electric field.

			By contrast, '''insulators''' have a large band gap, so electrons cannot reach the conduction band, which is why there is a net electric field inside an insulator at equilibrium and polarization occurs instead. '''Semiconductors''' have a moderate band gap, usually less than 4 eV, allowing limited conduction depending on temperature, lending their use to fascinating applications inside our devices.

			[[File:Band gaps.gif\|500px]]

	===A Mathematical Model===		===A Mathematical Model===

	Ohm's Law of J = σE can be used to model the relationship of conductivity to electric current density where J is electric current density, σ is conductivity of the material, and E is electric field. This ~~is a generalized~~ form of the ~~well known V = IR~~.		====Microscopic Formulation====

			The total current I through a conductor of cross-sectional area A is: <math>I = nq v_d A</math>, where n = number of charge carriers (in this case, electrons), q = charge of each carrier (for electrons, q = -e, and v_d = drift velocity of the electrons

			====Macroscopic Formulation (Ohm's Law)====

			On a larger, circuit-level scale, the current through a conductor is related to the applied voltage V and the resistance R in Ohm's Law: <math>V = IR</math>. Resistance R depends on the material and geometry of the condcutor: <math>R = \rho \frac{L}{A}</math> where ρ is the materials' innate resistivity, L is the length of the conductor, and A is the conductor's cross-sectional area. Since conductivity is the inverse of resistivity, we can write: <math>J = σE</math> can be used to model the relationship of conductivity to electric current density, where J is electric current density, σ is conductivity of the material, and E is the applied electric field. This microscopic form of Ohm's law connects the atomic behavior of electrons to a measurable current and voltage.

	σ is larger for better conductors like metals and saltwater. For "perfect" conductors, σ approaches infinity. In this case, E would be zero since the current density J cannot be infinity.		σ is larger for better conductors like metals and saltwater. For "perfect" conductors, σ approaches infinity. In this case, E would be zero since the current density J cannot be infinity.
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	[[File:Electric conductivity equation.jpg\|400 px]]		[[File:Electric conductivity equation.jpg\|400 px]]

	~~Conductivity can also be explained as the inverse of resistivity. σ = 1/ρ where ρ is resistivity.~~

	===A Computational Model===		===A Computational Model===

Jbuzz at 03:20, 12 November 2025

2025-11-12T03:20:31Z

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	===A Microscopic Model===		===A Microscopic Model===
	Microscopically, conductors are made up of a lattice of '''positively charged nuclei''' surrounded by freely moving '''electrons''' throughout the material. These electrons are known as '''delocalized electrons''', meaning that they are not bound to any specific atom, instead moving randomly within the solid.		Microscopically, conductors are made up of a lattice of '''positively charged nuclei''' surrounded by freely moving '''electrons''' throughout the material. These electrons are known as '''delocalized electrons''', meaning that they are not bound to any specific atom, instead moving randomly within the solid.

			[[File:Electron Sea (Plasma).jpg\|300px]]

	When no external electric field is applied, the motion of these electrons is random, resulting in '''no net current'''. However, when an electric field is introduced, these electrons experience a force opposite the direction of the field and begin to drift slightly with a '''drift velocity'''. Although this drift velocity is small, the large amount of electrons collectively moving produces an observable '''electric current'''.		When no external electric field is applied, the motion of these electrons is random, resulting in '''no net current'''. However, when an electric field is introduced, these electrons experience a force opposite the direction of the field and begin to drift slightly with a '''drift velocity'''. Although this drift velocity is small, the large amount of electrons collectively moving produces an observable '''electric current'''.
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	There is a relationship between conductivity and temperature: as temperature increases, the amount of phonons, or what we can see as the vibration of atoms in the lattice, increases. This increased number of phonons scatters these freely moving electrons more frequently, increasing resistance, and therefore decreasing conductivity.		There is a relationship between conductivity and temperature: as temperature increases, the amount of phonons, or what we can see as the vibration of atoms in the lattice, increases. This increased number of phonons scatters these freely moving electrons more frequently, increasing resistance, and therefore decreasing conductivity.

	~~image goes here~~		From a quantum-mechanical and materials science perspective, the behavior of conductors is governed by their energy '''band structure'''. In solids, closely spaced atomic orbitals overlap to form continuous ranges of energy that are known as bands. In '''conductors (metals)''', the '''valence band''', which contains the outer (valence) electrons and the '''conduction band''' either overlap or have a nonexistent band gap. Because of this overlap, electrons can esaily move to higher-energy states and flow under even a weak electric field.

	===A Mathematical Model===		===A Mathematical Model===

Jbuzz at 03:11, 12 November 2025

2025-11-12T03:11:37Z

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	'''David Nam Spring 2025''', Claimed/Edited by Jacob Buzzard Fall 2025		Created by '''David Nam Spring 2025''', Claimed/Edited by '''Jacob Buzzard Fall 2025'''

	==The Main Idea==		==The Main Idea==
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	** When a neutral conductor is placed in an external electric field, its free electrons shift opposite the field's direction. This creates a region of excess '''negative charge''' on one side and excess '''positive charge''' on the other. Though the conductor remains overall neutral (as charge is conserved), this '''polarization''' allows it to interact with nearby charges.		** When a neutral conductor is placed in an external electric field, its free electrons shift opposite the field's direction. This creates a region of excess '''negative charge''' on one side and excess '''positive charge''' on the other. Though the conductor remains overall neutral (as charge is conserved), this '''polarization''' allows it to interact with nearby charges.
	* Uniform potential inside conducting objects		* Uniform potential inside conducting objects
			** Since charges move freely within the conductor until equilibrium is reached, every point inside a conductor shares the same electric potential, in other words, the potential is uniform. At equilibrium, this means no current flows within the conductor, and the potential difference between any two points inside the conductor is '''zero'''.

	Conductors are essential to the flow of electric current in circuits. When connected to a voltage source, like a battery, the applied potential difference drives electrons through the conductor, producing a measurable current. The ability of a material to conduct depends on its atomic structure, external temperature, and geometry. Metals such as Cu, Ag, and Al are excellent conductors due to their high density of free electrons.		Conductors are essential to the flow of electric current in circuits. When connected to a voltage source, like a battery, the applied potential difference drives electrons through the conductor, producing a measurable current. The ability of a material to conduct depends on its atomic structure, external temperature, and geometry. Metals such as Cu, Ag, and Al are excellent conductors due to their high density of free electrons.
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	[[File:Conductor chart.gif\|600 px]]		[[File:Conductor chart.gif\|600 px]]

			===A Microscopic Model===
			Microscopically, conductors are made up of a lattice of '''positively charged nuclei''' surrounded by freely moving '''electrons''' throughout the material. These electrons are known as '''delocalized electrons''', meaning that they are not bound to any specific atom, instead moving randomly within the solid.

			When no external electric field is applied, the motion of these electrons is random, resulting in '''no net current'''. However, when an electric field is introduced, these electrons experience a force opposite the direction of the field and begin to drift slightly with a '''drift velocity'''. Although this drift velocity is small, the large amount of electrons collectively moving produces an observable '''electric current'''.

			There is a relationship between conductivity and temperature: as temperature increases, the amount of phonons, or what we can see as the vibration of atoms in the lattice, increases. This increased number of phonons scatters these freely moving electrons more frequently, increasing resistance, and therefore decreasing conductivity.

			image goes here

	===A Mathematical Model===		===A Mathematical Model===