Sign of Potential Difference - Revision history

Tquill at 02:23, 18 April 2016

2016-04-18T02:23:17Z

← Older revision		Revision as of 22:23, 17 April 2016
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	==References==		==References==
			G.W. Castellan, ''Physical Chemistry'', 3rd Ed., Addison-Wesley, Reading,MA, 1983

	Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4nd Edition by R. Chabay & B.Sherwood (John Wiley & Sons 2015) (pp.635-637)		Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4nd Edition by R. Chabay & B.Sherwood (John Wiley & Sons 2015) (pp.635-637)

Tquill at 02:21, 18 April 2016

2016-04-18T02:21:34Z

← Older revision		Revision as of 22:21, 17 April 2016
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	[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|left]]		[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|left]]
	As you can see in the diagram, the electric field lines point from A to B. Electric field lines point from regions on high potential to low potential. This means that point A has a higher potential than point B. Since <math> \Delta V = V_{final} - V_{initial}</math>, then <math> \Delta V_{A \rightarrow B} = V_B -V_A </math>. We know that <math> V_{A}</math> is a greater value than <math> V_{B}</math>, so their difference would give a negative value.		As you can see in the diagram, the electric field lines point from A to B. Electric field lines point from regions on high potential to low potential. This means that point A has a higher potential than point B. Since <math> \Delta V = V_{final} - V_{initial}</math>, then <math> \Delta V_{A \rightarrow B} = V_B -V_A </math>. We know that <math> V_{A}</math> is a greater value than <math> V_{B}</math>, so their difference would give a negative value.


	[[File:Potential_diff.jpg]]		[[File:Potential_diff.jpg]]

			Note that for this scenario, the same methodology and logic can be used to determine the sign of the potential difference of points A and B. However, this scenario also includes point C, which is parrallel to point B relative to its distance along the electric field lines. Thus, neither C or B has a higher potential than the other, and their potential difference is consequently zero.

	===A Mathematical Model===		===A Mathematical Model===

Tquill at 02:17, 18 April 2016

2016-04-18T02:17:43Z

← Older revision		Revision as of 22:17, 17 April 2016
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	The general procedure for this type of problem is to calculate the change in potential energy and then use that to determine the potential difference based on the sign, and magnitude of the charge. It is also important to recognize how despite the potential energy changes for the proton and electron were of opposite sign, the sign of the potential difference is only positive. The potential difference does not care about the sign of the charge in question.		The general procedure for this type of problem is to calculate the change in potential energy and then use that to determine the potential difference based on the sign, and magnitude of the charge. It is also important to recognize how despite the potential energy changes for the proton and electron were of opposite sign, the sign of the potential difference is only positive. The potential difference does not care about the sign of the charge in question.

	===~~Visual~~ Model===		===A Computational Model===
	'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.		'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.
	[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|left]]		[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|left]]
	As you can see in the diagram, the electric field lines point from A to B. Electric field lines point from regions on high potential to low potential. This means that point A has a higher potential than point B. Since <math> \Delta V = V_{final} - V_{initial}</math>, then <math> \Delta V_{A \rightarrow B} = V_B -V_A </math>. We know that <math> V_{A}</math> is a greater value than <math> V_{B}</math>, so their difference would give a negative value.		As you can see in the diagram, the electric field lines point from A to B. Electric field lines point from regions on high potential to low potential. This means that point A has a higher potential than point B. Since <math> \Delta V = V_{final} - V_{initial}</math>, then <math> \Delta V_{A \rightarrow B} = V_B -V_A </math>. We know that <math> V_{A}</math> is a greater value than <math> V_{B}</math>, so their difference would give a negative value.

			[[File:Potential_diff.jpg]]

	===A Mathematical Model===		===A Mathematical Model===

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	:<math>\Delta x</math> in the opposite direction of <math>\vec{E}</math>: positvie		:<math>\Delta x</math> in the opposite direction of <math>\vec{E}</math>: positvie
	:<math>\Delta x</math> is perpendicular to the direction of <math>\vec{E}</math>: <math>\Delta V</math>=0		:<math>\Delta x</math> is perpendicular to the direction of <math>\vec{E}</math>: <math>\Delta V</math>=0

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

	~~[[File:Potential_diff.jpg]]~~

	==Examples==		==Examples==

Tquill at 00:08, 18 April 2016

2016-04-18T00:08:45Z

← Older revision		Revision as of 20:08, 17 April 2016
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	===Visual Model===		===Visual Model===
	'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.		'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.
	[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|~~center~~]]		[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|left]]
			As you can see in the diagram, the electric field lines point from A to B. Electric field lines point from regions on high potential to low potential. This means that point A has a higher potential than point B. Since <math> \Delta V = V_{final} - V_{initial}</math>, then <math> \Delta V_{A \rightarrow B} = V_B -V_A </math>. We know that <math> V_{A}</math> is a greater value than <math> V_{B}</math>, so their difference would give a negative value.
	===A Mathematical Model===		===A Mathematical Model===

Tquill at 20:06, 17 April 2016

2016-04-17T20:06:45Z

← Older revision		Revision as of 16:06, 17 April 2016
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	===Visual Model===		===Visual Model===
	'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.		'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.
	[[File:~~sign_potential_difference~~.jpg\|thumb\|upright=2.5\|center]]		[[File:wikiupload_pot_diff.jpg\|thumb\|upright=2.5\|center]]

	===A Mathematical Model===		===A Mathematical Model===

Tquill at 20:02, 17 April 2016

2016-04-17T20:02:48Z

← Older revision		Revision as of 16:02, 17 April 2016
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	===Visual Model===		===Visual Model===
	'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.		'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.
			[[File:sign_potential_difference.jpg\|thumb\|upright=2.5\|center]]
	[[File:sign_potential_difference.jpg]]

	===A Mathematical Model===		===A Mathematical Model===

Tquill at 19:54, 17 April 2016

2016-04-17T19:54:43Z

← Older revision		Revision as of 15:54, 17 April 2016
Line 37:		Line 37:
	===Visual Model===		===Visual Model===
	'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.		'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.

	[[File:sign_potential_difference.jpg]]		[[File:sign_potential_difference.jpg]]

Tquill at 19:44, 17 April 2016

2016-04-17T19:44:34Z

← Older revision		Revision as of 15:44, 17 April 2016
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	The general procedure for this type of problem is to calculate the change in potential energy and then use that to determine the potential difference based on the sign, and magnitude of the charge. It is also important to recognize how despite the potential energy changes for the proton and electron were of opposite sign, the sign of the potential difference is only positive. The potential difference does not care about the sign of the charge in question.		The general procedure for this type of problem is to calculate the change in potential energy and then use that to determine the potential difference based on the sign, and magnitude of the charge. It is also important to recognize how despite the potential energy changes for the proton and electron were of opposite sign, the sign of the potential difference is only positive. The potential difference does not care about the sign of the charge in question.

			===Visual Model===
			'''Electric field lines always point from a region of high potential to a region of low potential.''' If given a diagram of a problem, draw the electric field lines and the sign of the potential difference can be found by <math> final - initial</math>.
			[[File:sign_potential_difference.jpg]]

	===A Mathematical Model===		===A Mathematical Model===

Tquill at 19:32, 17 April 2016

2016-04-17T19:32:44Z

← Older revision		Revision as of 15:32, 17 April 2016
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	==The Main Idea==		==The Main Idea==
			The potential difference is a quantity that represents a change in electric potential energy that a particle would experience moving through a region. Its most important quality is that it is independent of the charge in question. Multiplying the potential difference by the charge would yield the potential energy change said particle experiences. This relation is mathematically given by:
			<math>\Delta U</math> = <math>\Delta V\cdot q</math>

	By determining the direction of particle's path relative to the direction of electric field, the sign of potential difference can then be determined. The sign of the potential difference then shows if there is an increase or a decrease in potential energy, and a ~~resulting~~ change as in the kinetic energy.		Another useful form of potential difference can be represented by <math>\Delta V</math> = -<math>\vec{E}</math>●<math>\Delta \vec{x}</math>.
			By determining the direction of particle's path relative to the direction of electric field, the sign of potential difference can then be determined. The sign of the potential difference then shows if there is an increase or a decrease in potential energy, and a consequent change in the kinetic energy.

	~~===A Conceptual Approach===~~		Note that both of these explanations for Potential Difference are valid and are useful in different scenarios.
	~~The potential difference is a quantity~~ that ~~represents an electric potential energy change a particle would experience moving through a region. Its most important quality is that it is independent~~ of ~~the charge in question. Multiplying the potential difference by the charge would yield the potential energy change said particle experiences. This relation is mathematically given by:~~
	~~<math>\Delta U</math> = <math>\Delta V\cdot q</math>~~

	~~This means that an increase in potential energy~~ for an electron, a negative charge, gives a negative potential difference. It is very important to remember that the sign of the charge is very important when it comes to potential difference. For simplicity, let's imagine that we have a proton. If the proton experiences an increase in potential energy (perhaps it moved closer to another positive point charge), then the corresponding potential difference would be positive because the proton ended up with more potential energy than it started with (Recall:<math>\Delta V</math> = final state- initial state), and ~~the charge of the proton is positive. If an electron underwent the exact same process: experiences an increase~~ in ~~potential energy, the potential difference would indeed be negative due to the sign of the charge of an electron~~.

			===An Energetic Approach===
	The total energy of a closed, insulated system (Just fancy thermodynamic terms that mean there is no exchange of particles with the surroundings and there is no heat flow) can be given by the following equation:		The total energy of a closed, insulated system (Just fancy thermodynamic terms that mean there is no exchange of particles with the surroundings and there is no heat flow) can be given by the following equation:
	<math>\Delta K</math> + <math>\Delta U</math> = <math>\Delta W</math>, where <math>\Delta K</math> is the change in kinetic energy, <math>\Delta U</math> is the change in potential energy, and <math>\Delta W</math> is the amount of work done. In just about every scenario in this course, the work done will be equal to zero, so the we are left with:		<math>\Delta K</math> + <math>\Delta U</math> = <math>\Delta W</math>, where <math>\Delta K</math> is the change in kinetic energy, <math>\Delta U</math> is the change in potential energy, and <math>\Delta W</math> is the amount of work done. In just about every scenario in this course, the work done will be equal to zero, so the we are left with:
	<math>\Delta K</math> + <math>\Delta U</math> = 0		<math>\Delta K</math> + <math>\Delta U</math> = 0
	This equation is simply ~~stating~~ that a decrease in the kinetic energy of a particle means an increase in the potential energy of the particle. Using this ~~relation ship~~ will allow one to better understand more complex problems of potential difference with moving particles.		This equation simply states that a decrease in the kinetic energy of a particle means an equal and opposite increase in the potential energy of the particle (energy is conserved). Using this relationship will allow one to better understand more complex problems of potential difference with moving particles and energy changes.


			'''Example:''' A proton moves through a region of uniform electric field from point A to point B. While doing so, the proton's speed increases from 2,000 m/s to 4,300 m/s. Determine the potential difference between the proton's initial position and final position, and calculate the change in potential energy that an electron would experience moving through the same path.

			1) Find the change in kinetic energy the proton experiences:
			<math>\Delta KE</math> = <math> KE_{final} - KE_{initial}</math>, and since <math>KE</math>= <math> 1 \over 2</math> <math>\cdot m \cdot (v^2)</math>, we have:

			<math>\Delta KE</math> =<math> 1 \over 2</math> <math>\cdot m \cdot (v_{final}^2 -v_{initial}^2)</math>.
			Plugging in the numbers from the problem give: <math>\Delta KE</math> = <math> 1.210 \cdot 10^{-20} J</math> (recall that the mass of a proton is <math>1.67 \cdot 10^{-27} Kg</math>)

			2) This change is equal and opposite of the change in potential energy of the proton. Thus the potential energy change is equal to <math> -1.210 \cdot 10^{-20} J</math>

			3) Rearranging <math>\Delta U</math> = <math>\Delta V\cdot q</math>, we find that the potential difference <math> \Delta V_{A \rightarrow B} </math> = <math> \Delta U \over q_{proton} </math>. This gives us a potential difference ( <math> \Delta V_{A \rightarrow B} </math> ) of <math> -0.07562 </math> Volts

			4) We now have the potential difference, so calculating the change in potential energy that an electron would experience moving from A to B is simple. We know the following relationship <math>\Delta U</math> = <math>\Delta V\cdot q</math> and have already solved for the value of <math> \Delta V_{A \rightarrow B} </math>, and the charge of an electron is known. Thus, multiplying these quantities gives us a <math> \Delta U_{A \rightarrow B} = 1.210 \cdot 10^{-20}J </math>

			The general procedure for this type of problem is to calculate the change in potential energy and then use that to determine the potential difference based on the sign, and magnitude of the charge. It is also important to recognize how despite the potential energy changes for the proton and electron were of opposite sign, the sign of the potential difference is only positive. The potential difference does not care about the sign of the charge in question.

	===A Mathematical Model===		===A Mathematical Model===

Tquill at 08:04, 17 April 2016

2016-04-17T08:04:38Z

@@ Line 5: / Line 5: @@
 ==The Main Idea==
-By determining the direction of path relative to the direction of electric field, the sign of potential difference can then be determined. The sign of potential difference then shows if there is an increase or a decrease in potential energy, as well as kinetic energy.
+By determining the direction of  particle's path relative to the direction of electric field, the sign of potential difference can then be determined. The sign of the potential difference then shows if there is an increase or a decrease in potential energy, and a resulting change as in the kinetic energy.
 ===A Mathematical Model===