Coulomb's law - Revision history

Spencer B.: /* History */

2023-11-29T18:36:19Z

History

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	== History ==		== History ==
	Coulomb's Law was first formulated in 1785 in France by Charles Augustin de Coulomb. It was formulated using experimental evidence from a torsion balance. See [[https://en.wikipedia.org/wiki/Coulomb%27s_law 3]]. Later, when Maxwell formulated his laws of electromagnetism, it was found to be a special case of the more general Maxwell's ~~equation~~, which ~~applies~~ even when the charges are moving.		Coulomb's Law was first formulated in 1785 in France by Charles Augustin de Coulomb. It was formulated using experimental evidence from a torsion balance. See [[https://en.wikipedia.org/wiki/Coulomb%27s_law 3]]. Later, when Maxwell formulated his laws of electromagnetism, it was found to be a special case of the more general Maxwell's equations, which apply even when the charges are moving. Specifically, as mentioned above, Coulomb's Law is an easy consequence of Gauss's law of electric flux.

	== See Also ==		== See Also ==

Spencer B.: /* History */

2023-11-29T18:35:36Z

History

← Older revision		Revision as of 14:35, 29 November 2023
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	== History ==		== History ==
	Coulomb's Law was first formulated in 1785 in France by Charles Augustin de Coulomb. It was formulated using experimental evidence from a torsion balance. See [[https://en.wikipedia.org/wiki/Coulomb%27s_law 3]].		Coulomb's Law was first formulated in 1785 in France by Charles Augustin de Coulomb. It was formulated using experimental evidence from a torsion balance. See [[https://en.wikipedia.org/wiki/Coulomb%27s_law 3]]. Later, when Maxwell formulated his laws of electromagnetism, it was found to be a special case of the more general Maxwell's equation, which applies even when the charges are moving.


	== See Also ==		== See Also ==

Spencer B.: /* Example */

2023-11-29T18:34:28Z

Example

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	'''Difficult'''		'''Difficult'''

	Derive a formula for the magnitude of the electric field a distance <math>r</math> away from an infinite line of charges, spaced out with charge density <math>\rho</math> ~~C/m~~.		Derive a formula for the magnitude of the electric field a distance <math>r</math> away from an infinite line of charges, spaced out with charge density <math>\rho</math>.

Spencer B. at 18:34, 29 November 2023

2023-11-29T18:34:04Z

← Older revision		Revision as of 14:34, 29 November 2023
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	'''Difficult'''		'''Difficult'''

	Derive a formula for the magnitude of the electric field a distance <math>r</math> away from an infinite line of charges, spaced out with charge density <math>\rho</math>C/m.		Derive a formula for the magnitude of the electric field a distance <math>r</math> away from an infinite line of charges, spaced out with charge density <math>\rho</math> C/m.

Spencer B. at 18:32, 29 November 2023

2023-11-29T18:32:11Z

← Older revision		Revision as of 14:32, 29 November 2023
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	'''A Mathematical Model'''		'''A Mathematical Model'''

	According to [1], <math>\vec{F}_{on1} = {\frac{q_{1}q_{2}}{4\pi\epsilon_{0}\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>. <math>\epsilon_{0}</math>, the electric permittivity of free space, has a value of <math>\epsilon_{0} = 8.8541878128\times10^-12</math> F/m according to [2]. <math>\frac{1}{4\pi\epsilon_{0}}</math> can be conveniently approximated as <math>9\times10^9</math>, as is done in [1]. Thus Coulomb's Law is sometimes written as <math>\vec{F}_{on1} = {\frac{kq_{1}q_{2}}{\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>, where <math>k = 9\times10^9</math>. Moreover, if we define the ''electric field'' <math>\vec{E}</math> as the force felt per unit charge as a result of Coulomb's Law, then we can write Coulomb's Law as <math>\vec{E} = \frac{q}{4\pi\epsilon_{0}\|\vec{r}\|^2}\hat{r}</math>, where <math>\vec{r}</math> is the vector distance between the charge and the point in space at which the electric field is being measured. Also, if we have many charges <math>q_{1},...,q_{j}</math>, we can write Coulomb's Law as <math>\vec{E} = \sum_{n=0}^{j} {\frac{q_{n}}{4\pi\epsilon_{0}\|\vec{r}_{n}\|^2}}\hat{r}_{n}</math>, where <math>\vec{r}_{n}</math> is the distance to the <math>n</math>th charge. A unit of charge is called a Coulomb, and all charges are measured in Coulombs. An electron has <math>1.602\times10^-19</math> C of charge.		According to [[https://www.feynmanlectures.caltech.edu/II_04.html 1]], <math>\vec{F}_{on1} = {\frac{q_{1}q_{2}}{4\pi\epsilon_{0}\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>. <math>\epsilon_{0}</math>, the electric permittivity of free space, has a value of <math>\epsilon_{0} = 8.8541878128\times10^-12</math> F/m according to [[https://physics.nist.gov/cgi-bin/cuu/Value?ep0 2]]. <math>\frac{1}{4\pi\epsilon_{0}}</math> can be conveniently approximated as <math>9\times10^9</math>, as is done in [1]. Thus Coulomb's Law is sometimes written as <math>\vec{F}_{on1} = {\frac{kq_{1}q_{2}}{\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>, where <math>k = 9\times10^9</math>. Moreover, if we define the ''electric field'' <math>\vec{E}</math> as the force felt per unit charge as a result of Coulomb's Law, then we can write Coulomb's Law as <math>\vec{E} = \frac{q}{4\pi\epsilon_{0}\|\vec{r}\|^2}\hat{r}</math>, where <math>\vec{r}</math> is the vector distance between the charge and the point in space at which the electric field is being measured. Also, if we have many charges <math>q_{1},...,q_{j}</math>, we can write Coulomb's Law as <math>\vec{E} = \sum_{n=0}^{j} {\frac{q_{n}}{4\pi\epsilon_{0}\|\vec{r}_{n}\|^2}}\hat{r}_{n}</math>, where <math>\vec{r}_{n}</math> is the distance to the <math>n</math>th charge. A unit of charge is called a Coulomb, and all charges are measured in Coulombs. An electron has <math>1.602\times10^-19</math> C of charge.


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	== History ==		== History ==
	Coulomb's Law was first formulated in 1785 in France by Charles Augustin de Coulomb. It was formulated using experimental evidence from a torsion balance. See [3].		Coulomb's Law was first formulated in 1785 in France by Charles Augustin de Coulomb. It was formulated using experimental evidence from a torsion balance. See [[https://en.wikipedia.org/wiki/Coulomb%27s_law 3]].

Spencer B.: /* Main Idea */

2023-11-29T18:29:27Z

Main Idea

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	'''A Computational Model'''		'''A Computational Model'''

	~~I have~~ [https://www.glowscript.org/#/user/sboebel3012/folder/MyPrograms/program/Electronorbitingproton(classicaltheoryofatoms)/edit ~~created~~ a model] of an electron orbiting a proton using Coulomb's law. To see the electron orbit the proton, click the "Run Program" button at the top of the linked page.		Here is [https://www.glowscript.org/#/user/sboebel3012/folder/MyPrograms/program/Electronorbitingproton(classicaltheoryofatoms)/edit a model] of an electron orbiting a proton using Coulomb's law. To see the electron orbit the proton, click the "Run Program" button at the top of the linked page.

	== Example ==		== Example ==

Spencer B.: /* Main Idea */

2023-11-29T18:28:50Z

Main Idea

← Older revision		Revision as of 14:28, 29 November 2023
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	'''A Computational Model'''		'''A Computational Model'''

	I have [https://www.glowscript.org/#/user/sboebel3012/folder/MyPrograms/program/Electronorbitingproton(classicaltheoryofatoms)/edit created a model] of an electron orbiting a proton using Coulomb's law.		I have [https://www.glowscript.org/#/user/sboebel3012/folder/MyPrograms/program/Electronorbitingproton(classicaltheoryofatoms)/edit created a model] of an electron orbiting a proton using Coulomb's law. To see the electron orbit the proton, click the "Run Program" button at the top of the linked page.

	== Example ==		== Example ==

Spencer B.: /* Main Idea */

2023-11-29T18:27:57Z

Main Idea

← Older revision		Revision as of 14:27, 29 November 2023
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	'''A Computational Model'''		'''A Computational Model'''

			I have [https://www.glowscript.org/#/user/sboebel3012/folder/MyPrograms/program/Electronorbitingproton(classicaltheoryofatoms)/edit created a model] of an electron orbiting a proton using Coulomb's law.

	== Example ==		== Example ==

Spencer B.: /* Example */

2023-11-29T16:46:44Z

Example

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	''Solution.'' Find the vector distance between the two charges <math>\vec{r}_{12} = \vec{r}_{2} - \vec{r}_{1} = <4,3,0></math> m. Find the magnitude <math>\|\vec{r}_{12}\| = 5</math> and unit vector <math>\hat{r}_{12} = \frac{\vec{r}_{12}}{\|\vec{r}_{12}\|} = <\frac{4}{5},\frac{3}{5},0></math> m. Plug into Coulomb's Law <math>\vec{F}_{2on1} = {\frac{kq_{1}q_{2}}{\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>, we get <math>\vec{F}_{2on1} = {\frac{(9\times10^9)\times(-10)\times(5)}{25}}<\frac{4}{5},\frac{3}{5},0> = <-1.44\times10^{10},-1.08\times10^{10,0></math> N.		''Solution.'' Find the vector distance between the two charges <math>\vec{r}_{12} = \vec{r}_{2} - \vec{r}_{1} = <4,3,0></math> m. Find the magnitude <math>\|\vec{r}_{12}\| = 5</math> and unit vector <math>\hat{r}_{12} = \frac{\vec{r}_{12}}{\|\vec{r}_{12}\|} = <\frac{4}{5},\frac{3}{5},0></math> m. Plug into Coulomb's Law <math>\vec{F}_{2on1} = {\frac{kq_{1}q_{2}}{\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>, we get <math>\vec{F}_{2on1} = {\frac{(9\times10^9)\times(-10)\times(5)}{25}}<\frac{4}{5},\frac{3}{5},0> = <-1.44\times10^{10},-1.08\times10^{10},0></math> N.

	'''Middling'''		'''Middling'''

Spencer B.: /* Example */

2023-11-29T16:46:18Z

Example

← Older revision		Revision as of 12:46, 29 November 2023
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	''Solution.'' Find the vector distance between the two charges <math>\vec{r}_{12} = \vec{r}_{2} - \vec{r}_{1} = <4,3,0></math> m. Find the magnitude <math>\|\vec{r}_{12}\| = 5</math> and unit vector <math>\hat{r}_{12} = \frac{\vec{r}_{12}}{\|\vec{r}_{12}\|} = <\frac{4}{5},\frac{3}{5},0></math> m. Plug into Coulomb's Law <math>\vec{F}_{2on1} = {\frac{kq_{1}q_{2}}{\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>, we get <math>\vec{F}_{2on1} = {\frac{(9\times10^9)\times(-10)\times(5)}{25}}<\frac{4}{5},\frac{3}{5},0> = <-1.44\times10^10,-1.08\times10^10,0></math> N.		''Solution.'' Find the vector distance between the two charges <math>\vec{r}_{12} = \vec{r}_{2} - \vec{r}_{1} = <4,3,0></math> m. Find the magnitude <math>\|\vec{r}_{12}\| = 5</math> and unit vector <math>\hat{r}_{12} = \frac{\vec{r}_{12}}{\|\vec{r}_{12}\|} = <\frac{4}{5},\frac{3}{5},0></math> m. Plug into Coulomb's Law <math>\vec{F}_{2on1} = {\frac{kq_{1}q_{2}}{\|\vec{r}_{12}\|^2}}\hat{r}_{12}</math>, we get <math>\vec{F}_{2on1} = {\frac{(9\times10^9)\times(-10)\times(5)}{25}}<\frac{4}{5},\frac{3}{5},0> = <-1.44\times10^{10},-1.08\times10^{10,0></math> N.

	'''Middling'''		'''Middling'''