Potential Difference Path Independence - Revision history

Amandalanghauser at 21:01, 1 December 2015

2015-12-01T21:01:27Z

← Older revision		Revision as of 17:01, 1 December 2015
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			By: Amanda L

	The potential difference <math>\Delta V = V_B - V_A</math> between two locations A and B does not depend on the path taken between the locations.		The potential difference <math>\Delta V = V_B - V_A</math> between two locations A and B does not depend on the path taken between the locations.

	~~Claimed alanghauser3~~
	==The Main Idea==		==The Main Idea==

Amandalanghauser at 21:00, 1 December 2015

2015-12-01T21:00:58Z

← Older revision		Revision as of 17:00, 1 December 2015
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	<math>\Delta V = V_b + V_w = emf + (-EL) = 0</math>		<math>\Delta V = V_b + V_w = emf + (-EL) = 0</math>

	~~==History==~~

	~~Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.~~		== See also ==

			Electric Field of a Point Charge

	~~== See also ==~~		Electric Field of a Capacitor

	~~Are there related topics or categories~~ in ~~this wiki resource for the curious reader to explore? How does this topic fit into that context?~~		Potential Difference in a Uniform Field

	~~===Further reading===~~		Potential Difference of a point charge in a non-Uniform Field

	~~Books, Articles or other print media on this topic~~

	===External links===		===External links===

	~~Internet resources on this topic~~		http://www.physicsclassroom.com/class/circuits/Lesson-1/Electric-Potential-Difference

			https://en.wikipedia.org/wiki/Voltage

	==References==		==References==

	~~This section contains the the references you used while writing this page~~		Chabay, R., & Sherwood, B. (2015). Electric Potential. In Matter & interactions (4th ed., Vol. Two, pp. 644 - 648). Danvers, Massachusetts: J. Wiley & sons.

	[[Category:Which Category did you place this in?]]		[[Category:Which Category did you place this in?]]

Amandalanghauser: /* Connectedness */

2015-12-01T20:48:22Z

Connectedness

← Older revision		Revision as of 16:48, 1 December 2015
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	Therefore:		Therefore:
	<math>\Delta V = V_b + V_w = emf + (-EL) = 0</math>		<math>\Delta V = V_b + V_w = emf + (-EL) = 0</math>

	~~==Connectedness==~~
	~~#How is this topic connected to something that you are interested in?~~
	~~#How is it connected to your major?~~
	~~#Is there an interesting industrial application?~~

	==History==		==History==

Amandalanghauser: /* Round Trip Potential Difference */

2015-12-01T20:46:50Z

Round Trip Potential Difference

← Older revision		Revision as of 16:46, 1 December 2015
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	Therefore:		Therefore:
	<math>\Delta V = ~~V_(battery)~~ + ~~V_(wire)~~ = emf + (-EL) = 0</math>		<math>\Delta V = V_b + V_w = emf + (-EL) = 0</math>

	==Connectedness==		==Connectedness==

Amandalanghauser: /* Round Trip Potential Difference */

2015-12-01T20:45:32Z

Round Trip Potential Difference

← Older revision		Revision as of 16:45, 1 December 2015
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	Therefore:		Therefore:
	<math>\Delta V = ~~V_battery~~ + ~~V_wire~~ = emf + (-EL) = 0</math>		<math>\Delta V = V_(battery) + V_(wire) = emf + (-EL) = 0</math>

	==Connectedness==		==Connectedness==

Amandalanghauser: /* Round Trip Potential Difference */

2015-12-01T20:44:38Z

Round Trip Potential Difference

← Older revision		Revision as of 16:44, 1 December 2015
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	Take for example this very simple circuit:		Take for example this very simple circuit:
	[[File:circuit.png\|thumb\|none\|alt=Potential Difference Path Independence\|Simple Circuit]]		[[File:circuit.png\|thumb\|none\|alt=Potential Difference Path Independence\|Simple Circuit]]

			The potential produced by the battery is equivalent to its <math>emf</math>.

			Since circuits obey the conservation of energy the potential difference across the whole circuit must equal <math>0</math>

			Therefore:
			<math>\Delta V = V_battery + V_wire = emf + (-EL) = 0</math>

	==Connectedness==		==Connectedness==

Amandalanghauser: /* Difficult */

2015-12-01T20:37:57Z

Difficult

← Older revision		Revision as of 16:37, 1 December 2015
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	<math>= \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_2} - \frac{1}{r_1})</math>		<math>= \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_2} - \frac{1}{r_1})</math>

	===~~Difficult~~===		===Round Trip Potential Difference===
			Since the only points that matter when calculating the potential difference are the initial and final locations, then the round trip potential of any path will equal <math>0</math> since the initial and final locations are the same.

			Take for example this very simple circuit:
			[[File:circuit.png\|thumb\|none\|alt=Potential Difference Path Independence\|Simple Circuit]]

	==Connectedness==		==Connectedness==

Amandalanghauser: /* Two Different Paths Near a Point Charge */

2015-12-01T20:21:50Z

Two Different Paths Near a Point Charge

← Older revision		Revision as of 16:21, 1 December 2015
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	From <math>B</math> to <math>C</math>:		From <math>B</math> to <math>C</math>:
	<math>\Delta V_3 = 0</math>, since <math>\vec{E}</math> is perpendicular to <math>Delta l</math>.		<math>\Delta V_3 = 0</math>, since <math>\vec{E}</math> is perpendicular to <math>\Delta l</math>.

	From C to <math>f</math>:		From C to <math>f</math>:

Amandalanghauser: /* Two Different Paths Near a Point Charge */

2015-12-01T20:21:21Z

Two Different Paths Near a Point Charge

← Older revision		Revision as of 16:21, 1 December 2015
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	===Two Different Paths Near a Point Charge===		===Two Different Paths Near a Point Charge===
	Along a straight path from a point charge Q we know that		Along a straight path from a point charge Q we know that
	<math>\Delta V = \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{~~r_f~~} - \frac{1}{~~r_i~~})</math>		<math>\Delta V = \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_2} - \frac{1}{r_1})</math>

	'''''Path 2'''''		'''''Path 2'''''
	[[File:figure16.32.png\|thumb\|none\|alt=Potential Difference Path Independence\|Complicated Path]]		[[File:figure16.32.png\|thumb\|none\|alt=Potential Difference Path Independence\|Complicated Path]]
	From the initial point <math>i</math> to point <math>A</math>, <math>\vec{E}</math> is perpendicular to <math>\Delta l</math> so <math>\Delta V_1 = 0</math>		From the initial point <math>i</math> to point <math>A</math>, <math>\vec{E}</math> is perpendicular to <math>\Delta l</math> so <math>\Delta V_1 = 0</math>

			From <math>A</math> to <math>B</math>:
			<math>\Delta V_2 = \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_3} - \frac{1}{r_1})</math>

			From <math>B</math> to <math>C</math>:
			<math>\Delta V_3 = 0</math>, since <math>\vec{E}</math> is perpendicular to <math>Delta l</math>.

			From C to <math>f</math>:
			<math>\Delta V_4 = \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_2} - \frac{1}{r_3})</math>

			To find <math>V_f - V_i</math> add up all the <math>\Delta V's</math>

			<math>V_f - V_i = \Delta V_1 + \Delta V_2 + \Delta V_3 + \Delta V_4</math>

			<math>= 0 + \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_3} - \frac{1}{r_1}) + 0 + \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_2} - \frac{1}{r_3})</math>

			<math>= \frac{1}{4 \pi \epsilon_0 }Q(\frac{1}{r_2} - \frac{1}{r_1})</math>

	===Difficult===		===Difficult===

Amandalanghauser: /* Two Different Paths Near a Point Charge */

2015-12-01T20:09:51Z

Two Different Paths Near a Point Charge

← Older revision		Revision as of 16:09, 1 December 2015
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	'''''Path 2'''''		'''''Path 2'''''
	[[File:figure16.32\|thumb\|none\|alt=Potential Difference Path Independence\|Complicated Path]]		[[File:figure16.32.png\|thumb\|none\|alt=Potential Difference Path Independence\|Complicated Path]]
			From the initial point <math>i</math> to point <math>A</math>, <math>\vec{E}</math> is perpendicular to <math>\Delta l</math> so <math>\Delta V_1 = 0</math>

	===Difficult===		===Difficult===