Magnetic Force in a Moving Reference Frame - Revision history

Pvollrath3 at 02:45, 25 April 2022

2022-04-25T02:45:13Z

← Older revision		Revision as of 22:45, 24 April 2022
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	[[File:gammaFunc.png\|thumb]]		[[File:gammaFunc.png\|thumb]]

	''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''		''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame. Also I tried to upload two different images, but the wiki page keeps throwing up images. The first is a graph of the value of gamma as a function of velocity, which I generated in python using matplotlib, and the second is just a picture pulled from the internet of magnetic field lines. ''

Pvollrath3 at 02:39, 25 April 2022

2022-04-25T02:39:55Z

← Older revision		Revision as of 22:39, 24 April 2022
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	[[File:gammaFunc.png\|thumb~~\|Gamma as a function of Velocity~~]]		[[File:gammaFunc.png\|thumb]]

	''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''		''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''

Pvollrath3 at 02:39, 25 April 2022

2022-04-25T02:39:25Z

← Older revision		Revision as of 22:39, 24 April 2022
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	<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>		<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

	Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light.		Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light. The reason for this is that the value of gamma is almost exactly 1 until the particle's velocity approaches the speed of light, at which point it asymptotically goes to infinity at the speed of light. A graph of the value of gamma as a function of velocity is shown below.

	newVel = (partVel + refVel)/(1 - (partVelrefVel)/c*2)		newVel = (partVel + refVel)/(1 - (partVelrefVel)/c*2)


			[[File:gammaFunc.png\|thumb\|Gamma as a function of Velocity]]

	''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''		''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''

Pvollrath3 at 02:29, 25 April 2022

2022-04-25T02:29:39Z

← Older revision		Revision as of 22:29, 24 April 2022
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	newVel = (partVel + refVel)/(1 - (partVelrefVel)/c*2)		newVel = (partVel + refVel)/(1 - (partVelrefVel)/c*2)


			''Note: Linked code does not run in the Wiki page, but can be copy pasted into another code IDE and run without issue. Code returns the force on a particle moving in a constant magnetic field adjusted to be measured with reference to an inputed reference frame.''

Pvollrath3 at 20:56, 24 April 2022

2022-04-24T20:56:45Z

← Older revision		Revision as of 16:56, 24 April 2022
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	print(magneticForce(partVel))		print(magneticForce(partVel))
	''		''

			This code does not make any relativistic adjustments for velocity, as it assumes a particle is moving much slower than the speed of light. However, relativistic adjustments can be made simply by including a <math>\gamma</math> term when calculating the velocity of the moving particle in the new reference frame. Since as a vector sum of two velocities (as is the case when switching reference frame) in relativistic cases can be represented by the following;

			<math> \vec{v} + \vec{u} = \frac{\vec{v} + \vec{u}}{1 - \frac{\vec{v}\vec{u}}{c^2}} </math>

			Adding the code snipped below adjusts the prior code to make relativistic adjustments - Noting that the effects of special relativity are always present, but insignificant when the velocities are much lower than the speed of light.

			newVel = (partVel + refVel)/(1 - (partVelrefVel)/c*2)

Pvollrath3 at 20:47, 24 April 2022

2022-04-24T20:47:40Z

← Older revision		Revision as of 16:47, 24 April 2022
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	qCharge = 1		qCharge = 1

	print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")		print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
	xRef = input("V_x = ")		xRef = input("V_x = ")
	yRef = input("V_y = ")		yRef = input("V_y = ")
	zRef = input("V_z = ")		zRef = input("V_z = ")
	refVel = np.array([xRef,yRef,zRef],float)		refVel = np.array([xRef,yRef,zRef],float)

	def magneticForce(velocity):		def magneticForce(velocity):
	velocity -= refVel		velocity -= refVel
	return qCharge * np.cross(velocity,magStrength)		return qCharge * np.cross(velocity,magStrength)

	print(magneticForce(partVel))		print(magneticForce(partVel))
	''		''

Pvollrath3 at 20:47, 24 April 2022

2022-04-24T20:47:06Z

← Older revision		Revision as of 16:47, 24 April 2022
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	''		''
	import numpy as np		import numpy as np

	partVel = np.array([3,5,7],float)		partVel = np.array([3,5,7],float)
	magStrenght = np.array([0,0,1],float)		magStrenght = np.array([0,0,1],float)
	qCharge = 1		qCharge = 1

	print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")		print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")

Pvollrath3 at 20:46, 24 April 2022

2022-04-24T20:46:36Z

← Older revision		Revision as of 16:46, 24 April 2022
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	Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).		Magnetic force is easy to visualize because it takes only the speed and magnetic field with the right hand rule to calculate. However, the easiest way to visualize magnetic force in moving reference points is to imagine a car driving past and then imagine a car driving along side you. In the first case the car is the object that is moving. However, in the second case because the reference frame is moving alongside the observed object there is no change (if going the exact same speed).

	Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code ~~computes the magnitude~~ of ~~the magnetic force on~~ a ~~moving~~ particle ~~with~~ reference ~~to an observer moving with any inputed~~ velocity relative to ~~the~~ stationary ~~observer~~.		Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code is written in python and makes use of python's Numpy module to calculate a simple cross product of a particle's velocity, after accounting for a change in reference frame. The code is shown below.

			''
			import numpy as np

			partVel = np.array([3,5,7],float)
			magStrenght = np.array([0,0,1],float)
			qCharge = 1

			print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")
			xRef = input("V_x = ")
			yRef = input("V_y = ")
			zRef = input("V_z = ")
			refVel = np.array([xRef,yRef,zRef],float)

			def magneticForce(velocity):
			velocity -= refVel
			return qCharge * np.cross(velocity,magStrength)

			print(magneticForce(partVel))
			''

Pvollrath3 at 20:32, 24 April 2022

2022-04-24T20:32:53Z

← Older revision		Revision as of 16:32, 24 April 2022
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	~~import numpy as np~~		[[File:/Desktop/code.jpg\|thumb\|Simulated image of magnetic field lines]]

	~~partVel = np.array([3,5,7],float)~~
	~~magStrenght = np.array([0,0,1],float)~~
	~~qCharge = 1~~

	~~print("Input reference frame velocity relative to stationary reference frame (V_x,V_y,V_z)")~~
	~~xRef = input("V_x = ")~~
	~~yRef = input("V_y = ")~~
	~~zRef = input("V_z = ")~~
	~~refVel = np.array([xRef,yRef,zRef],float)~~

	~~def magneticForce(velocity):~~
	~~velocity -= refVel~~
	~~return qCharge * np.cross(velocity,magStrength)~~

	~~print(magneticForce(partVel))~~


	[[File:~~magnetic~~.~~jpeg~~\|thumb\|Simulated image of magnetic field lines]]
	==Examples==		==Examples==

Pvollrath3 at 20:30, 24 April 2022

2022-04-24T20:30:30Z

← Older revision		Revision as of 16:30, 24 April 2022
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	Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code computes the magnitude of the magnetic force on a moving particle with reference to an observer moving with any inputed velocity relative to the stationary observer.		Computationally, determining magnetic field strength with reference to moving reference frames, to say determine the force due to a magnetic field on a particle moving in that reference frame, is very simple. The following code computes the magnitude of the magnetic force on a moving particle with reference to an observer moving with any inputed velocity relative to the stationary observer.

	~~<math>~~
	import numpy as np		import numpy as np

Line 79:		Line 79:

	print(magneticForce(partVel))		print(magneticForce(partVel))
	~~</math>~~

	[[File:magnetic.jpeg\|thumb\|Simulated image of magnetic field lines]]		[[File:magnetic.jpeg\|thumb\|Simulated image of magnetic field lines]]