VPython Modelling of Electric and Magnetic Forces - Revision history

Yjia67: I have expanded on the specifics of mathematical and computational models of electric and magnetic forces. I made a VPython example for electric forces, and I also commented on the VPython code to show what each step actually does. Connectedness

2017-11-30T04:42:29Z

I have expanded on the specifics of mathematical and computational models of electric and magnetic forces. I made a VPython example for electric forces, and I also commented on the VPython code to show what each step actually does. Connectedness

← Older revision		Revision as of 00:42, 30 November 2017
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			===Electric Force Model===

			[http://www.glowscript.org/#/user/JJ129816/folder/Private/program/electricForce ElectricForceModel]

	===Magnetic Force Model===		===Magnetic Force Model===
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	[http://www.glowscript.org/#/user/griffinbonnett/folder/Public/program/vPython MagForceModel]		[http://www.glowscript.org/#/user/griffinbonnett/folder/Public/program/vPython MagForceModel]

			[[File:MagForcePic.JPG]]

	For Magnetic forces:		For Magnetic forces:
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	Due to our understanding of how magnetic fields cause a force on a moving charged particle, we can craft a general outline for the calculations. We can also find expected values and predict the behavior of the model. We will need to calculate the magnetic force and use it to update its position and velocity.		Due to our understanding of how magnetic fields cause a force on a moving charged particle, we can craft a general outline for the calculations. We can also find expected values and predict the behavior of the model. We will need to calculate the magnetic force and use it to update its position and velocity.




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	'''Initialize the variables'''		'''Initialize the variables'''
	B0 = vector(0,1,0)		B0 = vector(0,1,0) ''#initial magnetic field''
	particle = sphere(pos=(0, 0,.3), radius = .01, color = color.red)		particle = sphere(pos=(0, 0,.3), radius = .01, color = color.red) ''#create particle and set initial position''
	velocity = vector(2e6,1e6,0)		velocity = vector(2e6,1e6,0) ''#initial velocity''
	q = 1.6e-19		q = 1.6e-19 ''#constant: Coulombs of charge in one particle''
	m = 1.7e-27		m = 1.7e-27 ''#constant: mass of particle''
	trail = curve(color=particle.color)		trail = curve(color=particle.color) ''#establish visualization of the force''
	deltat = 1e-11		deltat = 1e-11 ''#time increments''
	t = 0		t = 0 ''#initial time''

	'''The Loop'''		'''The Loop'''
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	## Insert the necessary steps inside the loop below to update the particle's position and velocity		## Insert the necessary steps inside the loop below to update the particle's position and velocity
	## a)calculate the needed quantities to update the particle's velocity		## a)calculate the needed quantities to update the particle's velocity
	p = m * velocity		p = m * velocity
	Fnet= q * cross(velocity, B0)		Fnet= q * cross(velocity, B0)
	p = p + Fnet*deltat		p = p + Fnet*deltat
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	==Connectedness==		==Connectedness==
	#How is this topic connected to something that you are interested in?		#How is this topic connected to something that you are interested in?
	I am fascinated by 3D modeling. I have begun to teach my self Blender recently. Even though there is less programming involved, Blender incorporates much of the fundamentals that VPython uses such as vector math and using iterations of functions to achieve the desired output.		::I am fascinated by 3D modeling. I have begun to teach my self Blender recently. Even though there is less programming involved, Blender incorporates much of the fundamentals that VPython uses such as vector math and using iterations of functions to achieve the desired output. I believe that computational models are great learning aids for people to visualize concepts in 3D, such as electric and magnetic fields and forces, especially when the path becomes complex and more mathematical iterations are required.

	#How is it connected to your major?		#How is it connected to your major?
	VPython, electric and magnetic forces, and simulations are fundamental to my major as an electrical engineer. I can use Vpython to simulate how certain electrical components that would interact ~~in an~~ magnetic field. I could also use it to simulate the electromagnetic interactions at the quantum level.		::VPython, electric and magnetic forces, and simulations are fundamental to my major as an electrical engineer. I can use Vpython to simulate how certain electrical components that would interact with a magnetic field. I could also use it to simulate the electromagnetic interactions at the quantum level.

	#Is there an interesting industrial application?		#Is there an interesting industrial application?
	Industry routinely uses VPython to simulate optimal efficiency. This can give a baseline to test the efficiency of industrial machines or processes. These simulations can help identify ways to improve the bottom line of a company. The simulations can also save money in research and development by replacing some more costly experimental testing.		::Industry routinely uses VPython to simulate optimal efficiency. This can give a baseline to test the efficiency of industrial machines or processes. These simulations can help identify ways to improve the bottom line of a company. The simulations can also save money in research and development by replacing some more costly experimental testing.

	==History==		==History==

Yjia67 at 04:28, 30 November 2017

2017-11-30T04:28:17Z

← Older revision		Revision as of 00:28, 30 November 2017
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	:''in the loop, you will (not all steps are included depending on the problem)''		:''in the loop, you will (not all steps are included depending on the problem)''
	::1. update electric / magnetic fields if they are time-variant		::i. update electric / magnetic fields if they are time-variant
	::2. update electric / magnetic forces		::ii. update electric / magnetic forces
	::3. update momentum / velocity if the observed target is a moving object		::iii. update momentum / velocity if the observed target is a moving object
	::4. update particle position		::iv. update particle position

	A finished and working program will give us the ability to visualize the physics of magnetic and electric forces. Vpython can be used to model any number of other physical interactions as well such as springs and gravity. Running a simulation allows us to view concepts that would not be observable any other way especially on the same timescale. We are able to visibly observe magnetic and electric fields in a dynamic situation which is difficult to visualize without a model. This also allows for many more calculations to be performed and the ability to interpolate and extrapolate data.		A finished and working program will give us the ability to visualize the physics of magnetic and electric forces. Vpython can be used to model any number of other physical interactions as well such as springs and gravity. Running a simulation allows us to view concepts that would not be observable any other way especially on the same timescale. We are able to visibly observe magnetic and electric fields in a dynamic situation which is difficult to visualize without a model. This also allows for many more calculations to be performed and the ability to interpolate and extrapolate data.

Yjia67 at 04:25, 30 November 2017

2017-11-30T04:25:56Z

@@ Line 34: / Line 34: @@
 ===A Computational Model===
-This is when we begin to program using Vpython. A finished and working program will give us the ability to visualize the physics of magnetic and electric forces. Vpython can be used to model any number of other physical interactions as well such as springs and gravity. Running a simulation allows us to view concepts that would not be observable any other way especially on the same time scale. We are able to visibly observe magnetic and electric fields in a dynamic situation which is difficult to visualize without a model.  This also allows for many more calculations to be preformed and the ability to interpolate and extrapolate data.
+This is when we begin to program using Vpython.
 ==Examples==

Yjia67 at 22:50, 29 November 2017

2017-11-29T22:50:27Z

← Older revision		Revision as of 18:50, 29 November 2017
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	===A Mathematical Model===		===A Mathematical Model===
	When starting a new Vpython program, first write out all the equations and constants you might need~~. Define~~ the variables in their appropriate forms such as vectors, arrows, or spheres.
			When you are starting a new Vpython program, first write out all the equations and constants you might need, and then define the variables in their appropriate forms such as vectors, arrows, or spheres.


	:''Electric Force''		:''Electric Force''
	::<math>\vec F={q}_{2}\times\vec{E}_{1} </math>		::<math>\vec F={q}_{2}\times\vec{E}_{1} </math>

	::~~[[File:equationsForElectricFields.PNG\|thumb\|~~equations for electric fields(vec{E})]]		::equations for electric fields(vec{E})
			::[[File:equationsForElectricFields.PNG]]
	::[http://www.physicsbook.gatech.edu/Electric_Force derivation]		::[http://www.physicsbook.gatech.edu/Electric_Force derivation]

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	::<math>{\vec{F} = q\vec{v}\times\vec{B}}</math>		::<math>{\vec{F} = q\vec{v}\times\vec{B}}</math>

	::~~[[File:equationsForMagneticFields.PNG\|thumb\|~~equations for magnetic fields(vec{B})]]		::equations for magnetic fields(vec{B})
			::[[File:equationsForMagneticFields.PNG]]
	::[http://www.physicsbook.gatech.edu/Magnetic_Force derivation]		::[http://www.physicsbook.gatech.edu/Magnetic_Force derivation]

	The equations ~~above~~ are the mathematical basis for the VPython ~~code and simulations~~.
			The equations are the mathematical basis for computational simulations. After defining constants and initializing variables in the initial state, you can now mathematically update the position, electric/magnetic field, electric/magnetic force in the next small time step. In order to show this at different times and/or locations, you can simply iterate the same process with the new values. Since it is an iterated process, VPython can only give us an approximate model. To display time-varying electric or magnetic field, one can decrease the time increment in each step to make the approximation more accurate.


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

Yjia67 at 22:34, 29 November 2017

2017-11-29T22:34:47Z

← Older revision		Revision as of 18:34, 29 November 2017
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	:''Electric Force''		:''Electric Force''
	::<math>\vec F={q}_{2}\times\vec{E}_{1} </math>		::<math>\vec F={q}_{2}\times\vec{E}_{1} </math>

			::[[File:equationsForElectricFields.PNG\|thumb\|equations for electric fields(vec{E})]]
	::[http://www.physicsbook.gatech.edu/Electric_Force derivation]		::[http://www.physicsbook.gatech.edu/Electric_Force derivation]


	:''Magnetic Force''		:''Magnetic Force''
	::<math>{\vec{F} = q\vec{v}\times\vec{B}}</math>		::<math>{\vec{F} = q\vec{v}\times\vec{B}}</math>

			::[[File:equationsForMagneticFields.PNG\|thumb\|equations for magnetic fields(vec{B})]]
	::[http://www.physicsbook.gatech.edu/Magnetic_Force derivation]		::[http://www.physicsbook.gatech.edu/Magnetic_Force derivation]

			The equations above are the mathematical basis for the VPython code and simulations.

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

Yjia67 at 22:21, 29 November 2017

2017-11-29T22:21:07Z

← Older revision		Revision as of 18:21, 29 November 2017
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	:''Electric Force''		:''Electric Force''
	::<math>\vec F={q}_{2}\vec{E}_{1} </math>		::<math>\vec F={q}_{2}\times\vec{E}_{1} </math>
	::[http://www.physicsbook.gatech.edu/Electric_Force derivation]		::[http://www.physicsbook.gatech.edu/Electric_Force derivation]

Yjia67 at 22:20, 29 November 2017

2017-11-29T22:20:52Z

← Older revision		Revision as of 18:20, 29 November 2017
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	:''Electric Force''		:''Electric Force''
	::<math>\|\vec F\|=~~\frac{1}{4 \pi \epsilon_0 } \frac{\|{q}_{1}{q}_{2}\|}{r^2}=\|{q}_{2}\|\frac{1}{4 \pi \epsilon_0 } \frac{\|{q}_{1}\|}{r^2}=\|~~{q}_{2}\|\|\vec{E}_{1}\| </math>		::<math>\vec F={q}_{2}\vec{E}_{1} </math>
	::[http://www.physicsbook.gatech.edu/Electric_Force derivation]		::[http://www.physicsbook.gatech.edu/Electric_Force derivation]


	:''Magnetic Force''		:''Magnetic Force''

Yjia67 at 22:19, 29 November 2017

2017-11-29T22:19:48Z

← Older revision		Revision as of 18:19, 29 November 2017
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	When starting a new Vpython program, first write out all the equations and constants you might need. Define the variables in their appropriate forms such as vectors, arrows, or spheres.		When starting a new Vpython program, first write out all the equations and constants you might need. Define the variables in their appropriate forms such as vectors, arrows, or spheres.

			:''Electric Force''
			::<math>\|\vec F\|=\frac{1}{4 \pi \epsilon_0 } \frac{\|{q}_{1}{q}_{2}\|}{r^2}=\|{q}_{2}\|\frac{1}{4 \pi \epsilon_0 } \frac{\|{q}_{1}\|}{r^2}=\|{q}_{2}\|\|\vec{E}_{1}\| </math>
			::[http://www.physicsbook.gatech.edu/Electric_Force derivation]

			:''Magnetic Force''
			::<math>{\vec{F} = q\vec{v}\times\vec{B}}</math>
			::[http://www.physicsbook.gatech.edu/Magnetic_Force derivation]

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

Yjia67 at 22:13, 29 November 2017

2017-11-29T22:13:40Z

← Older revision		Revision as of 18:13, 29 November 2017
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	===A Mathematical Model===		===A Mathematical Model===
	When ~~you start~~ a new Vpython program, ~~you should~~ first write out all the equations and constants you might need.~~You should also define any~~ variables ~~you use~~ in their appropriate forms such as vectors, arrows, or spheres. ~~Then, you should get a rough outline of what values need to be calculated and how the constants and equations can be best applied for the calculations.~~		When starting a new Vpython program, first write out all the equations and constants you might need. Define the variables in their appropriate forms such as vectors, arrows, or spheres.



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

Yjia67 at 22:07, 29 November 2017

2017-11-29T22:07:08Z

← Older revision		Revision as of 18:07, 29 November 2017
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	VPython Modeling of Electric and Magnetic Forces		VPython Modeling of Electric and Magnetic Forces

	Claimed By: Griffin Bonnett Spring 2017 4/09/2017		Claimed By: Griffin Bonnett Spring 2017 4/09/2017

	Claimed by: Yunqing Jia Fall 2017		Claimed by: Yunqing Jia Fall 2017