Electric Potential - Revision history

Galmeida9: /* Further reading */

2025-04-14T00:42:12Z

Galmeida9: /* Connectedness */

2025-04-14T00:21:14Z

Connectedness

← Older revision		Revision as of 20:21, 13 April 2025
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	==Connectedness==		==Connectedness==
			Electric potential is deeply woven into many branches of physics and engineering, often acting as a unifying concept for understanding energy, fields, and forces in electrical systems.

			In electrostatics, potential provides an alternative to the electric field — rather than focusing on vector directions of force, potential simplifies analysis by using scalar values. This is especially powerful in systems with symmetry, where calculating potential is often much easier than finding the field directly.

			In circuits, electric potential becomes the more familiar voltage, representing the energy per unit charge available to move charges through components. The entire theory of DC and AC circuit analysis relies on understanding potential differences across resistors, capacitors, and inductors.

			In energy conservation, potential plays a key role. Just as gravitational potential energy helps us calculate the motion of falling objects, electric potential energy allows us to determine how charges move in electric fields. It’s one of the few concepts that links statics (equilibrium) and dynamics (motion) so seamlessly.

			In quantum mechanics, electric potential enters the Schrödinger equation, shaping potential wells, barriers, and quantum tunneling behavior — core features in everything from semiconductors to atomic structure.

			Even in materials science and chemistry, potential is central. Electrochemical potential drives redox reactions in batteries and electroplating, and molecular electrostatic potential maps help visualize where reactions will occur on a molecule. Therefore, it is extremely important to understand the fundamental of electric potential. It has many many uses.

	==History==		==History==

Galmeida9: /* Difficult */

2025-04-14T00:18:50Z

Difficult

← Older revision		Revision as of 20:18, 13 April 2025
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	===Difficult===		===Difficult===
			'''Problem:'''

			Three identical point charges
			+
			𝑞 are placed at the corners of an '''equilateral triangle''' of side length
			𝑎
			.
			A fourth point
			𝑃 is located directly above the '''centroid''' of the triangle at a vertical height
			ℎ
			.

			(a) Calculate the '''electric potential''' at point
			𝑃 due to the three charges.
			Express your answer in terms of
			𝑞
			,
			𝑎
			,
			ℎ
			, and physical constants.

			The electric potential due to a point charge is:

			<math>V = \frac{1}{4\pi \varepsilon_0} \cdot \frac{q}{r}</math>

			Since potential is a scalar, the total potential is just the sum of the contributions from each charge:

			<math>V = \sum_{i=1}^{3} \frac{1}{4\pi \varepsilon_0} \cdot \frac{q}{r_i}</math>

			Because point
			𝑃 lies directly above the centroid, each distance
			𝑟
			𝑖

			is the same.
			We calculate this using the Pythagorean theorem:

			The horizontal distance from any vertex to the centroid of an equilateral triangle is:

			<math>r_{\text{base}} = \frac{a}{\sqrt{3}}</math>

			Thus, the full distance from each charge to point
			𝑃
			P is:

			<math>r = \sqrt{r_{\text{base}}^2 + h^2} = \sqrt{\frac{a^2}{3} + h^2}</math>

			Plugging into the formula:

			<math> V = 3 \cdot \frac{1}{4\pi \varepsilon_0} \cdot \frac{q}{\sqrt{ \frac{a^2}{3} + h^2 }} </math>

			Final Answer

			<math> \boxed{ V = \frac{3q}{4\pi \varepsilon_0 \sqrt{ \frac{a^2}{3} + h^2 }} } </math>

	==Connectedness==		==Connectedness==

Galmeida9: Undo revision 47150 by Galmeida9 (talk)

2025-04-14T00:15:04Z

Undo revision 47150 by Galmeida9 (talk)

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 </div></div>
-\section*{Difficult Example: Electric Potential from Three Point Charges}
+===Difficult===
 ==Connectedness==

Galmeida9: /* Difficult */

2025-04-14T00:13:27Z

Difficult

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 </div></div>
-===Difficult===
+\section*{Difficult Example: Electric Potential from Three Point Charges}
 ==Connectedness==

Galmeida9: /* The Main Idea */

2025-04-13T23:38:17Z

The Main Idea

← Older revision		Revision as of 19:38, 13 April 2025
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	==References==		==References==


	~~== The Main Idea ==~~

	==Examples==		==Examples==

Galmeida9 at 21:01, 13 April 2025

2025-04-13T21:01:55Z

← Older revision		Revision as of 17:01, 13 April 2025
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	Claimed by ~~Neal Austensen Fall2023~~		Claimed by Gabriel Almeida Spring 2025
	==The Main Idea==		==The Main Idea==
	'''Electric Potential Energy''', like all forms of potential energy, is the potential for work to be done, in this case by the electric force. The '''Electric Potential''' (frequently referred to as voltage, from its SI unit, the Volt) is the '''Electric Potential Energy''' associated with the test charge (1 Coulomb), such that it depends only on the source, just as the electric field is related to the electric force, but depends only on the source. One may similarly remember the parallel concept of the gravitational potential, which was gravitational potential energy divided by mass.		'''Electric Potential Energy''', like all forms of potential energy, is the potential for work to be done, in this case by the electric force. The '''Electric Potential''' (frequently referred to as voltage, from its SI unit, the Volt) is the '''Electric Potential Energy''' associated with the test charge (1 Coulomb), such that it depends only on the source, just as the electric field is related to the electric force, but depends only on the source. One may similarly remember the parallel concept of the gravitational potential, which was gravitational potential energy divided by mass.

Naustensen3 at 22:27, 26 November 2023

2023-11-26T22:27:49Z

← Older revision		Revision as of 18:27, 26 November 2023
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			Claimed by Neal Austensen Fall2023
	==The Main Idea==		==The Main Idea==
	'''Electric Potential Energy''', like all forms of potential energy, is the potential for work to be done, in this case by the electric force. The '''Electric Potential''' (frequently referred to as voltage, from its SI unit, the Volt) is the '''Electric Potential Energy''' associated with the test charge (1 Coulomb), such that it depends only on the source, just as the electric field is related to the electric force, but depends only on the source. One may similarly remember the parallel concept of the gravitational potential, which was gravitational potential energy divided by mass.		'''Electric Potential Energy''', like all forms of potential energy, is the potential for work to be done, in this case by the electric force. The '''Electric Potential''' (frequently referred to as voltage, from its SI unit, the Volt) is the '''Electric Potential Energy''' associated with the test charge (1 Coulomb), such that it depends only on the source, just as the electric field is related to the electric force, but depends only on the source. One may similarly remember the parallel concept of the gravitational potential, which was gravitational potential energy divided by mass.

Jbates61: /* History */

2023-04-26T03:37:10Z

History

← Older revision		Revision as of 23:37, 25 April 2023
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	==History==		==History==

			The concept of electric potential has a long, illustrious history that dates back many centuries. Otto von Guericke, William Gilbert, and Robert Boyle were among the pioneering scientists who contributed to the study of electricity in the 17th century. The idea of electric potential did not start to take form until the 18th century, however.

			French scientist Charles Du Fay discovered in 1733 that friction could charge certain materials, including amber, and that this charge could be transmitted to other things. Du Fay also observed that depending on the sign of their charges, two charged items might either attract or repel one another when placed near to one another.

			[[File:lj.jpg\|center]]

			Both Dutch scientist Pieter van Musschenbroek and German physicist Ewald Georg von Kleist independently devised the Leyden jar, a device that could hold an electric charge, in 1745. The Leyden jar was simply a glass jar with a wire or rod put through the cork and either water or metal foil within. The charge would be kept in the jar until the wire was charged.

			Charles-Augustin de Coulomb, a French scientist, first proposed the idea of electric potential energy in 1785. In an electric field, Coulomb demonstrated that the amount of labor needed to transfer a charged particle from one location to another was proportional to the difference in electric potential between the two sites. In the 19th century, Scottish scientist James Clerk Maxwell and German physicist Georg Simon Ohm expanded on this idea.

			Electric potential is a key idea in physics today and is applied in a variety of domains, including electronics, electrical engineering, and the study of charged particle behavior in electromagnetic fields.

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

Ecarder: /* A Computational Model */

2022-10-12T01:16:45Z

A Computational Model

← Older revision		Revision as of 21:16, 11 October 2022
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	::[https://trinket.io/embed/glowscript/0a7e486c94 Teach hand-on with GlowScript]		::[https://trinket.io/embed/glowscript/0a7e486c94 Teach hand-on with GlowScript]

			Click the link below and press run to see a visual model of electric potential in space with equal and opposite charges (Press "Run")
			::[https://trinket.io/glowscript/7f354ee8e6?outputOnly=true 3D Electric Potential with GlowScript]

	Watch this video for a more visual approach!		Watch this video for a more visual approach!

@@ Line 299: / Line 299: @@
 ==See also==
-===Further reading===
+== Further Reading ==
 ===Externals links===