Combining Electric and Magnetic Forces - Revision history

Lpimentel3: /* Connectedness */

2018-11-25T06:13:22Z

Connectedness

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	The following VPython trinket module is a demonstration of a velocity selector. Two particles of different speeds pass through an area with perpendicular magnetic and electric fields. Within this trinket, you can change the initial values of the velocity selector and particle velocities to see how this affects the particles' motion as they try to pass through a circular area.		The following VPython trinket module is a demonstration of a velocity selector. Two particles of different speeds pass through an area with perpendicular magnetic and electric fields. Within this trinket, you can change the initial values of the velocity selector and particle velocities to see how this affects the particles' motion as they try to pass through a circular area.

	[[File:velocitySelector3Stages.jpg]]		[[File:velocitySelector3Stages.jpg\|thumb\| '''Figure 7.1.''' SImulation of a Velocity Selector ]]

	[https://trinket.io/glowscript/d3067081b7 Velocity Selector Trinket]		[https://trinket.io/glowscript/d3067081b7 Velocity Selector Trinket]

Lpimentel3: /* Applications */

2018-11-25T06:10:25Z

Applications

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 [[File:Velocityselector2.png|thumb| '''Figure 7.''' Illustration of a Velocity Selector ]]
-The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ).  Particles with the correct speed will be unaffected while other particles will be deflected. This technique is used in technologies such as electron microscopes and spectrometers.
+The Velocity Selector is a device used to filter particles based on their velocity. A Velocity Selector uses controlled, perpendicular, electric and magnetic fields to filter certain charged particles (See '''Figure 7''' ). These electric and magnetic fields exert a Lorentz force on the particle. For the particle to remain unaffected, the Lorentz force must be zero. Therefore, we have:
 '''''Electric Motor'''''

Lpimentel3 at 05:33, 25 November 2018

2018-11-25T05:33:10Z

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	Claimed by ~~Alana Kaplan (~~Fall~~, 2015); Claimed to Edit by Alexis Jacob (Spring, 2016 - ''Added middle~~ and ~~difficult examples, figures,~~ and ~~minor format changes'')~~		Claimed by Luis Pimentel Fall 2018
	~~Claimed by Ha Eun An (Fall 2016)~~		Edited the Velocity Selector section. Went into more detail about why this works and created a VPython trinket demonstrating and visualizing a velocity selector for particles.

	Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]] and [[Motional Emf]].		Though the pattern in which electric and magnetic forces interact with particles is observably different, their effects can be quantitatively be compared. The principle of adding the two functions of force as a net force is one that now serves as a fundamental principle of electromagnetics. It serves as a building block for many important Laws such as [[Hall Effect]] and [[Motional Emf]].

Han46: /* History */

2016-11-28T04:10:57Z

History

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	The relationship between electric and magnetic forces was first questioned in the mid-18th century when Johann Tobias Mayer (1760) and Henry Cavendish (1762) proposed that the force on magnetic poles and electrically charged objects followed the inverse-square law, which was proven to be true by Charles-Augustin in 1784.		The relationship between electric and magnetic forces was first questioned in the mid-18th century when Johann Tobias Mayer (1760) and Henry Cavendish (1762) proposed that the force on magnetic poles and electrically charged objects followed the inverse-square law, which was proven to be true by Charles-Augustin in 1784.

	Michael Faraday ~~proposed~~ the concept of electric and magnetic fields, ~~and~~ James Clerk Maxwell mathematically ~~proved~~ the concepts. In 1865, Maxwell's field equations consisted of some form of the Lorentz force equation, but at the time it was not clear how it related to forces on charged moving particles. J.J Thomson was the first to attempt a derivation of Maxwell's field equations, and he derived a basic form of the formula for the electromagnetic forces on a charged moving particle in relation to the properties of the particle and its external fields. In 1892, Hendrik Lorentz corrected mistakes of the old formula and derived the modern form of the equation, which contains the forces due to both electric and magnetic fields.		Following Michael Faraday's proposal of the concept of electric and magnetic fields, James Clerk Maxwell was first to mathematically prove the concepts. In 1865, Maxwell's field equations consisted of some form of the Lorentz force equation, but at the time it was not clear how it related to forces on charged moving particles. J.J Thomson was the first to attempt a derivation of Maxwell's field equations, and he derived a basic form of the formula for the electromagnetic forces on a charged moving particle in relation to the properties of the particle and its external fields. In 1892, Hendrik Lorentz corrected mistakes of the old formula and derived the modern form of the equation, which contains the forces due to both electric and magnetic fields.

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

Han46 at 04:09, 28 November 2016

2016-11-28T04:09:22Z

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	[[Inductance]]		[[Inductance]]

			==History==

			The relationship between electric and magnetic forces was first questioned in the mid-18th century when Johann Tobias Mayer (1760) and Henry Cavendish (1762) proposed that the force on magnetic poles and electrically charged objects followed the inverse-square law, which was proven to be true by Charles-Augustin in 1784.

			Michael Faraday proposed the concept of electric and magnetic fields, and James Clerk Maxwell mathematically proved the concepts. In 1865, Maxwell's field equations consisted of some form of the Lorentz force equation, but at the time it was not clear how it related to forces on charged moving particles. J.J Thomson was the first to attempt a derivation of Maxwell's field equations, and he derived a basic form of the formula for the electromagnetic forces on a charged moving particle in relation to the properties of the particle and its external fields. In 1892, Hendrik Lorentz corrected mistakes of the old formula and derived the modern form of the equation, which contains the forces due to both electric and magnetic fields.

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

Han46 at 03:52, 28 November 2016

2016-11-28T03:52:10Z

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	The Lorentz Force calculation is now a fundamental principle of electromagnetism.		The Lorentz Force calculation is now a fundamental principle of electromagnetism.

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

	Following are diagrams which display a uniform electric field in the +x direction and a uniform magnetic field in +y direction for a proton and an electron, with varying velocities.		Following are diagrams which display a uniform electric field in the +x direction and a uniform magnetic field in +y direction for a proton and an electron, with varying velocities.

Han46: /* Difficult */

2016-11-28T03:50:05Z

Difficult

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	:''Solution:''		:''Solution:''
	:Step 1: ''Direction of the Magnetic Force~~' '~~- Use right hand rule or <math> {\vec v \times\vec B} </math>. See '''Figure 6'''.		:Step 1: Direction of the Magnetic Force - Use right hand rule or <math> {\vec v \times\vec B} </math>. See '''Figure 6'''.
	:Step 2: ''Current through the resistor'' -		:Step 2: Current through the resistor -
	::: <math> {ΔV}_{round trip} = 0 </math>		::: <math> {ΔV}_{round trip} = 0 </math>
	::: <math> {{ΔV}_{round trip} + motional emf - {ΔV}_{resistor} = 0} </math>		::: <math> {{ΔV}_{round trip} + motional emf - {ΔV}_{resistor} = 0} </math>

Han46: /* Difficult */

2016-11-28T03:49:39Z

Difficult

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	:''Solution:''		:''Solution:''
	:Step 1: ''Direction of the Magnetic Force''- Use right hand rule or <math> {\vec v \times\vec B} </math>. See '''Figure 6'''.		:Step 1: ''Direction of the Magnetic Force' '- Use right hand rule or <math> {\vec v \times\vec B} </math>. See '''Figure 6'''.
	:Step 2: ''Current through the resistor''-		:Step 2: ''Current through the resistor'' -
	::: <math> {ΔV}_{round trip} = 0 </math>		::: <math> {ΔV}_{round trip} = 0 </math>
	::: <math> {{ΔV}_{round trip} + motional emf - {ΔV}_{resistor} = 0} </math>		::: <math> {{ΔV}_{round trip} + motional emf - {ΔV}_{resistor} = 0} </math>
	::: <math> motional emf = IR </math>		::: <math> motional emf = IR </math>
	::: <math> I = \frac {motional emf} {R} </math>		::: <math> I = \frac {motional emf} {R} </math>
	:~~Step 3~~: <math> {\|q\vec E\| = \|q\vec v\vec B\|} </math>, <math> {\|ΔV\| = IR} </math>		::: <math> {\|q\vec E\| = \|q\vec v\vec B\|} </math>, <math> {\|ΔV\| = IR} </math>
	::: <math> {qE = qvB} </math>		::: <math> {qE = qvB} </math>
	::: <math> E = vB </math>		::: <math> E = vB </math>

Han46: /* Difficult */

2016-11-28T03:48:42Z

Difficult

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	:Step 2: ''Current through the resistor''-		:Step 2: ''Current through the resistor''-
	::: <math> {ΔV}_{round trip} = 0 </math>		::: <math> {ΔV}_{round trip} = 0 </math>
	::: <math> {{ΔV}_{round trip} + motional emf - {ΔV}_{resistor}} </math>		::: <math> {{ΔV}_{round trip} + motional emf - {ΔV}_{resistor} = 0} </math>
	::: <math> motional emf = IR </math>		::: <math> motional emf = IR </math>
	::: <math> I = \frac {motional emf} {R} </math>		::: <math> I = \frac {motional emf} {R} </math>
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	::: <math> {qE = qvB} </math>		::: <math> {qE = qvB} </math>
	::: <math> E = vB </math>		::: <math> E = vB </math>
	::: <math> \|ΔV\| = E*ΔL = vBL </math>		::: <math> motional emf = \|ΔV\| = E*ΔL = vBL </math>
	::: <math> {I = \frac {vBL} {R}} </math>		::: <math> {I = \frac {vBL} {R}} </math>

Han46: /* Difficult */

2016-11-28T03:46:55Z

Difficult

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	:''Solution:''		:''Solution:''
	:Step 1: ''Direction of the Magnetic Force''- Use right hand rule ~~for~~ v ~~cross~~ B. See '''Figure 6'''.		:Step 1: ''Direction of the Magnetic Force''- Use right hand rule or <math> {\vec v \times\vec B} </math>. See '''Figure 6'''.
	:Step 2: ''Current through the resistor''-		:Step 2: ''Current through the resistor''-
	::: <math> {ΔV}_{round trip} = 0 </math>		::: <math> {ΔV}_{round trip} = 0 </math>