Point Charge - Revision history

Gcruz38: /* A Computational Model */

2025-11-24T03:59:46Z

A Computational Model

← Older revision		Revision as of 23:59, 23 November 2025
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	[[File:Code_2.png]]		[[File:Code_2.png]]

			===A Computational Model 2 ===

			[https://trinket.io/glowscript/650fbf3a95c5 Click this link to see another computional model.]

	==Examples==		==Examples==

Gcruz38: /* History */

2025-11-24T03:26:51Z

History

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	Charles de Coulomb was born in June 14, 1736 in central France. He spent much of his early life in the military and was placed in regions throughout the world. He only began to do scientific experiments out of curiously on his military expeditions. However, when controversy arrived with him and the French bureaucracy coupled with the French Revolution, Coulomb had to leave France and thus really began his scientific career.		Charles de Coulomb was born in June 14, 1736 in central France. He spent much of his early life in the military and was placed in regions throughout the world. He only began to do scientific experiments out of curiously on his military expeditions. However, when controversy arrived with him and the French bureaucracy coupled with the French Revolution, Coulomb had to leave France and thus really began his scientific career.

	Between 1785 and 1791, de Coulomb wrote several key papers centered around multiple relations of electricity and magnetism. This helped him develop the principle known as Coulomb's Law, which confirmed that the force between two electrical charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This is the same relationship that is seen in the electric field equation of a point charge.		Between 1785 and 1791, de Coulomb wrote several key papers centered around multiple relations of electricity and magnetism. This helped him develop the principle known as Coulomb's Law, which confirmed that the force between two electrical charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This is the same relationship that is seen in the electric field equation of a point charge.

			[[File:Benjamin-Franklin-Portrait.png]]
			''Benjamin Franklin''

			Benjamin Franklin (1706–1790) made several foundational contributions to the early understanding of electric charge. Although he did not write mathematical laws like Coulomb, his ideas directly shaped the concepts used in point-charge physics.

			Franklin introduced the naming system of positive and negative charge, which is still used today. He proposed that charge behaves like a conserved quantity that can move between objects—an essential idea behind treating charges as isolated point charges located at specific positions in space.

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

Gcruz38: Undo revision 47342 by Gcruz38 (talk)

2025-11-24T03:25:04Z

Undo revision 47342 by Gcruz38 (talk)

← Older revision		Revision as of 23:25, 23 November 2025
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	PEMF (Pulsed Electromagnetic Field) therapy's principle of restoring optimal voltage in damaged cells through electromagnetic fields has interesting parallels in aerospace engineering. For example, the management of electromagnetic fields is critical in spacecraft and aircraft to protect onboard electronics and enhance communication signals. The concept of PEMF can inspire the development of systems that can self-regulate and optimize electrical potential across different components of an aircraft or spacecraft, thereby enhancing performance and resilience. Such systems could prove vital in long-duration space missions, where human intervention is limited, and the machine's ability to self-heal and maintain operational integrity can be a game-changer.		PEMF (Pulsed Electromagnetic Field) therapy's principle of restoring optimal voltage in damaged cells through electromagnetic fields has interesting parallels in aerospace engineering. For example, the management of electromagnetic fields is critical in spacecraft and aircraft to protect onboard electronics and enhance communication signals. The concept of PEMF can inspire the development of systems that can self-regulate and optimize electrical potential across different components of an aircraft or spacecraft, thereby enhancing performance and resilience. Such systems could prove vital in long-duration space missions, where human intervention is limited, and the machine's ability to self-heal and maintain operational integrity can be a game-changer.

	==~~Historical Figures of Electricity==~~		==History==
			[[File:CoulombCharles300px.jpg]]
	~~===Charles de Coulomb=~~==
	[[File:CoulombCharles300px.jpg~~\|200px~~]]
	''Charles de Coulomb''		''Charles de Coulomb''

	Charles~~-Augustin~~ de Coulomb was born on June 14, 1736, in central France. ~~Early in~~ his life~~, he served~~ in the ~~French~~ military ~~engineering corps, where he~~ was ~~stationed~~ in ~~various~~ regions ~~around~~ the world. ~~During his military service, he~~ began ~~conducting~~ scientific ~~experiments—initially~~ out of ~~curiosity and practical necessity~~.		Charles de Coulomb was born in June 14, 1736 in central France. He spent much of his early life in the military and was placed in regions throughout the world. He only began to do scientific experiments out of curiously on his military expeditions. However, when controversy arrived with him and the French bureaucracy coupled with the French Revolution, Coulomb had to leave France and thus really began his scientific career.

	~~Political conflicts~~ with French bureaucracy ~~and the upheaval of~~ the French Revolution ~~eventually pushed~~ Coulomb ~~away from military life~~ and ~~into a more focused~~ scientific career. Between 1785 and 1791, he published several groundbreaking papers on electricity and magnetism. These works led to the formulation of Coulomb’s Law, establishing that the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This same relationship appears in the electric field expression for a point charge.

	~~Coulomb’s contributions laid essential foundations for both electrostatics and magnetostatics, shaping modern physics.~~

	~~---~~

	~~===Benjamin Franklin===~~
	~~[[File:Benjamin-Franklin-Portrait.png\|200px]]~~
	~~''Benjamin Franklin''~~

	Benjamin Franklin (1706–1790) was one of the earliest scientists to systematically study electricity. Although he was not a mathematician and did not write formal equations, his qualitative insights profoundly shaped the development of electrical theory.

	Franklin introduced the concept of positive and negative charge, which is still used today. He was also the first to propose that lightning was an electrical phenomenon. His famous kite experiment (1752) provided evidence that atmospheric lightning and laboratory electricity were the same, leading to his invention of the lightning rod—a practical device that is still used worldwide to safely redirect electrical discharges.

	Franklin also helped popularize the idea of charge conservation: the total amount of electric “fluid” (as he called it) remains constant, even as it flows from one object to another. This idea became a cornerstone of later electrical theory and supported the formal mathematical laws developed by scientists like Coulomb.

	~~Franklin’s blend~~ of ~~experimentation, intuition~~, and ~~practical invention helped build~~ the ~~early conceptual framework~~ that ~~modern electromagnetism grew from~~.		Between 1785 and 1791, de Coulomb wrote several key papers centered around multiple relations of electricity and magnetism. This helped him develop the principle known as Coulomb's Law, which confirmed that the force between two electrical charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This is the same relationship that is seen in the electric field equation of a point charge.

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

Gcruz38: /* History */

2025-11-24T03:24:36Z

History

← Older revision		Revision as of 23:24, 23 November 2025
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	PEMF (Pulsed Electromagnetic Field) therapy's principle of restoring optimal voltage in damaged cells through electromagnetic fields has interesting parallels in aerospace engineering. For example, the management of electromagnetic fields is critical in spacecraft and aircraft to protect onboard electronics and enhance communication signals. The concept of PEMF can inspire the development of systems that can self-regulate and optimize electrical potential across different components of an aircraft or spacecraft, thereby enhancing performance and resilience. Such systems could prove vital in long-duration space missions, where human intervention is limited, and the machine's ability to self-heal and maintain operational integrity can be a game-changer.		PEMF (Pulsed Electromagnetic Field) therapy's principle of restoring optimal voltage in damaged cells through electromagnetic fields has interesting parallels in aerospace engineering. For example, the management of electromagnetic fields is critical in spacecraft and aircraft to protect onboard electronics and enhance communication signals. The concept of PEMF can inspire the development of systems that can self-regulate and optimize electrical potential across different components of an aircraft or spacecraft, thereby enhancing performance and resilience. Such systems could prove vital in long-duration space missions, where human intervention is limited, and the machine's ability to self-heal and maintain operational integrity can be a game-changer.

	==~~History~~==		==Historical Figures of Electricity==
	[[File:CoulombCharles300px.jpg]]
			===Charles de Coulomb===
			[[File:CoulombCharles300px.jpg\|200px]]
	''Charles de Coulomb''		''Charles de Coulomb''

	Charles de Coulomb was born in June 14, 1736 in central France. ~~He spent much of~~ his ~~early~~ life in the military ~~and~~ was ~~placed~~ in regions ~~throughout~~ the world. ~~He only~~ began ~~to do~~ scientific ~~experiments~~ out of ~~curiously on his military expeditions~~. ~~However, when controversy arrived~~ with ~~him~~ and the ~~French bureaucracy coupled with~~ the French Revolution, ~~Coulomb had~~ to ~~leave France~~ and ~~thus really began~~ his ~~scientific career~~.		Charles-Augustin de Coulomb was born on June 14, 1736, in central France. Early in his life, he served in the French military engineering corps, where he was stationed in various regions around the world. During his military service, he began conducting scientific experiments—initially out of curiosity and practical necessity.

			Political conflicts with French bureaucracy and the upheaval of the French Revolution eventually pushed Coulomb away from military life and into a more focused scientific career. Between 1785 and 1791, he published several groundbreaking papers on electricity and magnetism. These works led to the formulation of Coulomb’s Law, establishing that the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This same relationship appears in the electric field expression for a point charge.

			Coulomb’s contributions laid essential foundations for both electrostatics and magnetostatics, shaping modern physics.

			---

			===Benjamin Franklin===
			[[File:Benjamin-Franklin-Portrait.png\|200px]]
			''Benjamin Franklin''

			Benjamin Franklin (1706–1790) was one of the earliest scientists to systematically study electricity. Although he was not a mathematician and did not write formal equations, his qualitative insights profoundly shaped the development of electrical theory.

			Franklin introduced the concept of positive and negative charge, which is still used today. He was also the first to propose that lightning was an electrical phenomenon. His famous kite experiment (1752) provided evidence that atmospheric lightning and laboratory electricity were the same, leading to his invention of the lightning rod—a practical device that is still used worldwide to safely redirect electrical discharges.

			Franklin also helped popularize the idea of charge conservation: the total amount of electric “fluid” (as he called it) remains constant, even as it flows from one object to another. This idea became a cornerstone of later electrical theory and supported the formal mathematical laws developed by scientists like Coulomb.

	~~Between 1785 and 1791~~, ~~de Coulomb wrote several key papers centered around multiple relations of electricity~~ and ~~magnetism. This~~ helped ~~him develop~~ the ~~principle known as Coulomb's Law, which confirmed~~ that the force between two electrical charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This is the same relationship that is seen in the electric field equation of a point charge.		Franklin’s blend of experimentation, intuition, and practical invention helped build the early conceptual framework that modern electromagnetism grew from.

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

Gcruz38: /* Difficult */

2025-11-24T03:11:09Z

Difficult

← Older revision		Revision as of 23:11, 23 November 2025
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	===Difficult===		===Difficult===
	The electric force on a -~~2mC~~ particle at a location (3.98 , 3.98 , 3.98) m due to a particle at the origin is <math>< -5.510^{3} , -5.510^{3}, -5.5*10^{3}></math> N. What is the charge on the particle at the origin?		The electric force on a -2 mC particle at location (3.98, 3.98, 3.98) m due to a particle at the origin is
			<math>\langle -5.5\times10^{3},\, -5.5\times10^{3},\, -5.5\times10^{3}\rangle</math> N.
			What is the charge on the particle at the origin?

	Given the force and charge on the particle, ~~one~~ can ~~calculate~~ the ~~surrounding~~ electric field~~. With this variable found, this problem becomes much like~~ the ~~last one~~.		Given the force and the charge of the particle experiencing the force, we can first compute the electric field at the observation location. Once the electric field is known, we can use the point-charge electric field model to solve for the unknown source charge.
	~~<math> E_{mag}= \frac{1}{4 \pi \epsilon_0 } \frac{q}{r_{mag}^2} </math> to find~~ the ~~rmag value. To find <math>\hat r</math>~~ we can ~~find the direction of~~ the electric field ~~as that is obviously going~~ to ~~be in~~ the ~~same direction as <math>\hat r</math>. Then, once we find <math>\hat r</math>, all that is left to do is multiply <math>\hat r</math> by rmag and that will give us the <math> r</math> vector~~. ~~We can then find the location of the particle as we know <math>r=r_{observation}-r_{particle}</math>~~

	<table border>		<table border>
	<tr>		<tr>
	<td> <b>Step 1.</b> Find the ~~magnitude of the Electric~~ field:		<td>
	<math> F = ~~Eq </math>~~		<b>Step 1.</b> Find the electric field using <math>\vec{F} = q\vec{E}</math>.
	~~<math> =~~ E * -2mC </math>

	<math> E = \frac{~~< -5.5e3 , -5.5e3, -5.5e3>~~}{~~-2mC~~}		<math>\vec{E} = \frac{\vec{F}}{q}</math>

			<math> = \frac{\langle -5.5\times10^{3}, -5.5\times10^{3}, -5.5\times10^{3}\rangle}{-2\times10^{-3}}</math>

	= <2.~~75e6~~ , 2.~~75e6~~, 2.~~75e6>~~ </math> N/C		<math> = \langle 2.75\times10^{6},\, 2.75\times10^{6},\, 2.75\times10^{6}\rangle</math> N/C
	</td></tr>		</td>
			</tr>

	<tr><td><b>Step 2:</b> ~~Find~~ <math>\vec ~~r_{obs} - \vec r_~~{~~particle~~} </math>.		<tr>
			<td>
			<b>Step 2.</b> Compute <math>\vec{r}</math> from the particle at the origin to the observation location.

	<math>\vec r = <3.98 , ~~3.98 , 3.98> m - <0 , 0~~ , ~~0> m = <~~3.98 , ~~3.98~~ , 3.98> m </math>		<math>\vec{r} = \langle 3.98,\,3.98,\,3.98\rangle\ \text{m}</math>

	~~To find <math>\vec r_{mag} </math>, find the magnitude of <math><3.98 , 3.98 , 3.98></math>~~		Magnitude:

	<math>\sqrt{3.98^2+3.98^2+3.98^2}=\sqrt{47.52}= 6.9</math>		<math>\|\vec{r}\| = \sqrt{3.98^2 + 3.98^2 + 3.98^2}</math>
	</td></tr>		<math>= \sqrt{47.52} \approx 6.89\ \text{m}</math>

			Unit vector:

			<math>\hat{r} = \frac{\vec{r}}{\|\vec{r}\|}</math>
			</td>
			</tr>

			<tr>
			<td>
			<b>Step 3.</b> Solve for the unknown charge using the point-charge field equation:

	~~<td> '''Step 3:''' Find '''''q''''' by rearranging the equation for~~ <math>E_{mag}</math>		<math>E_{mag}=\frac{1}{4\pi\epsilon_0}\frac{\|q\|}{r^2}</math>

	~~<math> E_{mag}= \frac{1}{4 \pi \epsilon_0 } \frac{q}{r^2} </math>~~		Rearranged:

	~~By rearranging this equation we get~~		<math>\|q\| = (4\pi\epsilon_0)\,(r^2)\,E_{mag}</math>

	<math> q= {4 pi * \~~epsilon_0 } {r~~^~~2}E_~~{~~mag~~} </math>		Using <math>E_{mag} = 2.75\times10^{6}</math> N/C and <math>r = 6.89</math> m:

	<math> q= {~~{1/~~(~~9e9)} {~~6.9^{2~~}}4~~.~~76e6~~} </math>		<math>\|q\| = (8.99\times10^{-12})(6.89^2)(2.75\times10^{6})</math>

	<math> q~~= +~~ 0.~~253~~ C </math~~></td~~>		<math>\|q\| \approx 0.237\ \text{C}</math>

			Sign of the charge:
			The force on the negative test charge is toward the origin → the source must be positive.

			<b>Final Answer:</b>
			<math>q_{\text{origin}} \approx +0.24\ \text{C}</math>
			</td>
			</tr>
	</table border>		</table border>

			====Common Mistakes====
			* Using the wrong sign for q.
			Remember: if the force on a negative charge points toward the origin, the source must be positive.

			* Forgetting that E and F point the same direction only for positive test charges.
			Since the test charge is −2 mC, is opposite the force direction.

			* Mixing up <math>\vec{r}</math> and <math>\|\vec{r}\|</math>.
			One is a vector; the other is a scalar distance.

			* Failing to use the magnitude of E when solving for \|q\|.
			The field equation uses only magnitudes, not vector components.

			* Using an incorrect value of Coulomb’s constant.

	==Connectedness==		==Connectedness==

Gcruz38: /* A Mathematical Model */

2025-11-24T02:48:52Z

A Mathematical Model

← Older revision		Revision as of 22:48, 23 November 2025
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	* r = distance from source location to observation location		* r = distance from source location to observation location
	* <math>\hat{r}</math> = unit vector pointing from the source to the observation point		* <math>\hat{r}</math> = unit vector pointing from the source to the observation point

			'''Reminder:''' <math>\hat{r}</math> always points from the source charge to the observation location.

	The direction of the electric field depends on the sign of the source charge:		The direction of the electric field depends on the sign of the source charge:
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	Coulomb’s Law describes the magnitude of the electric force between two point charges.		Coulomb’s Law describes the magnitude of the electric force between two point charges.

			The full vector form is:

			<math>\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{Q_1 Q_2}{r^2}\hat{r}</math>

	* <math>Q_1, Q_2</math> = the charges		* <math>Q_1, Q_2</math> = the charges
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	The force on a test charge is given by <math>F = Eq</math>.		The force on a test charge is given by <math>F = Eq</math>.

	Substituting Coulomb’s Law for F ~~produces~~:		Substituting Coulomb’s Law for F:

	<math> E = \frac{F}{q_2} = \frac{1}{4\pi\epsilon_0}\frac{q_1}{r^2}\hat{r} </math>		<math> E = \frac{F}{q_2} = \frac{1}{4\pi\epsilon_0}\frac{q_1}{r^2}\hat{r} </math>

			The similarity of the Coulomb force law and electric field equation comes from the fact that the electric field is the force per unit test charge:

			<math>\vec{E} = \frac{\vec{F}}{q_{test}}</math>

	Direction rules:		Direction rules:
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	[[File:IMG_1DCC0A11C7B8-1.jpeg]]		[[File:IMG_1DCC0A11C7B8-1.jpeg]]


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

Gcruz38 at 02:47, 24 November 2025

2025-11-24T02:47:42Z

← Older revision		Revision as of 22:47, 23 November 2025
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	Claimed by ~~Elena Rice Spring~~ 2025		Claimed by Gabriel Cruz Fall 2025

	This page is all about the [[Electric Field]] due to a Point Charge.		This page is all about the [[Electric Field]] due to a Point Charge.

Gcruz38: /* The Main Ideas */

2025-11-24T02:47:19Z

The Main Ideas

Show changes

Gcruz38: /* The Electric Field */

2025-11-24T02:42:51Z

The Electric Field

← Older revision		Revision as of 22:42, 23 November 2025
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	(Ch 13.3 in ''Matter & Interactions Vol. 2: Modern Mechanics, 4th Edition by R. Chabay & B. Sherwood'')		(Ch 13.3 in ''Matter & Interactions Vol. 2: Modern Mechanics, 4th Edition by R. Chabay & B. Sherwood'')

	~~In general, the~~ electric field ~~evaluates the affect of the~~ source on the ~~surrounding objects and area~~. ~~The electric~~ field ~~created by a charge is present throughout~~ space ~~at all times~~, whether or not ~~there is~~ another charge ~~around~~ to ~~feel its effects~~. ~~Therefore~~, ~~the concept of~~ the electric field ~~by a point charge describes the~~ interactions ~~that can happen~~ at a distance~~, due to these affects caused by this point charge~~.		The electric field describes how a source charge influences the space around it. This field exists everywhere in space, whether or not another charge is present to experience it. In other words, the electric field allows interactions to occur at a distance.

	~~Important~~ to ~~differentiate~~ that ~~Electric Force does~~ not ~~equal~~ the ~~Electric Field~~.		It is important to note that electric force is not the same as electric field.

	Electric Field of a Charge Observed at a location: \vec{F} = q\vec{E}		Electric Field of a Charge Observed at a location: <math>\vec{F} = q \vec{E}</math>
	*F = ~~Force~~ on particle		* F = force on the particle
	*E = electric field at ~~source~~ location		* E = electric field at the observation location
	*q = ~~magnitude~~ of the ~~charge of~~ particle (assume q= 1.6 x 10^-19 unless stated ~~otherewise~~)		* q = charge of the particle (assume (1.6 times 10^{-19}) C unless stated otherwise)
	The magnitude of the electric field decreases ~~with increasing~~ distance from the point charge.
			The magnitude of the electric field decreases as the distance from the point charge increases.

	<table border>		<table border>
	<tr>		<tr>
	<td>The electric field of a positive point charge points radially outward</td>		<td>The electric field of a positive point charge points radially outward.</td>
	<td>The electric field of a negative point charge points radially inward</td>		<td>The electric field of a negative point charge points radially inward.</td>
	</tr>		</tr>
	<tr>		<tr>
	<td>[[File:Proton_electric_field.png]] </td>		<td>[[File:Proton_electric_field.png]]</td>
	<td> [[File:Electron_electric_field.png]] </td>		<td>[[File:Electron_electric_field.png]]</td>
	</tr>		</tr>
	</table border>		</table border>

Gcruz38: /* The Electric Field */

2025-11-24T02:40:55Z

The Electric Field

← Older revision		Revision as of 22:40, 23 November 2025
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	Important to differentiate that Electric Force does not equal the Electric Field.		Important to differentiate that Electric Force does not equal the Electric Field.

	Electric Field of a Charge Observed at a location: F = Eq		Electric Field of a Charge Observed at a location: \vec{F} = q\vec{E}
	*F = Force on particle		*F = Force on particle
	*E = electric field at source location		*E = electric field at source location