Sign of a Potential Difference - Revision history

Yalmonte3: /* Harder Example */

2020-11-21T22:08:14Z

Harder Example

← Older revision		Revision as of 18:08, 21 November 2020
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	These questions are very simple as long as you ~~thing~~ methodically about what you are doing and always keep in mind two very important things:		These questions are very simple as long as you think methodically about what you are doing and always keep in mind two very important things:

	'''1)''' What is the initial and final for the particle's path? Again, '''dL is always final-initial'''!		'''1)''' What is the initial and final for the particle's path? Again, '''dL is always final-initial'''!

Jruan34: /* Real Life Example to Explain Sign of Potential Difference */

2018-11-24T22:12:05Z

Real Life Example to Explain Sign of Potential Difference

← Older revision		Revision as of 18:12, 24 November 2018
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	Now imagine if the same swimmer decided to test his endurance skills and swim upstream instead, or against the current. Now, the theoretical electrical field and change in location (dL) are opposing each other. This now means that the swimmer must exert a lot of his own energy to get from point A to B while opposing the current pushing against him. Looking at the energy in the scenario, the swimmer now has to provide a change in energy that he, himself, makes, so the potential difference would be positive. In reference to the swimmer, he is providing the energy as opposed to letting the current provide it like in the previous example. This shows that '''opposite directions''' mean a '''positive potential difference'''.		Now imagine if the same swimmer decided to test his endurance skills and swim upstream instead, or against the current. Now, the theoretical electrical field and change in location (dL) are opposing each other. This now means that the swimmer must exert a lot of his own energy to get from point A to B while opposing the current pushing against him. Looking at the energy in the scenario, the swimmer now has to provide a change in energy that he, himself, makes, so the potential difference would be positive. In reference to the swimmer, he is providing the energy as opposed to letting the current provide it like in the previous example. This shows that '''opposite directions''' mean a '''positive potential difference'''.

	Finally, imagine if you were swimming perpendicular to the current. Now, the dL and electrical field equivalents are '''running perpendicular to each other'''. The swimmer does not have to exert any more or less energy to get from point A to B because the current is not in the same dimension as the initial and final locations. This shows why '''potential difference = 0''' when the dot product of Electric Field and dL is carried out.		Finally, imagine if you were swimming perpendicular to the current. Now, the dL and electrical field equivalents are '''running perpendicular to each other'''. The swimmer does not have to exert any more or less energy to get from point A to B because the current is not in the same dimension as the initial and final locations. This shows why '''potential difference = 0''' when the dot product of Electric Field and dL is carried out.

			Another real-life example is to imagine you are carrying a ball and prepare to throw it from the building. If you go downstairs (the same direction as the gravity.), the potential of the ball you carry is decreasing, because when you throw it, it takes a shorter time to reach the ground. Thus this movement has a negative potential difference. So on so forth, if you go upstairs (opposite direction as the gravity), the potential increases because it takes a longer time for the ball to reach the ground and when it reaches it, it has a larger energy. Due to δpotential = final potential - initial potential, the potential difference is positive. From this example, again, we can conclude that "opposite directions" means positive potential difference and same direction means negative potential difference. It should be the same on gravity potential field and electrical potential field.

	== Easier Examples ==		== Easier Examples ==

Jruan34 at 21:58, 24 November 2018

2018-11-24T21:58:19Z

← Older revision		Revision as of 17:58, 24 November 2018
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	~~CLAIMED BY ANDRES BEGAZO (Fall 2017),~~ Junzhe Ruan(Fall 2018)		Claimed by Junzhe Ruan(Fall 2018)

Jruan34: /* Easier Examples */

2018-11-07T04:33:44Z

Easier Examples

← Older revision		Revision as of 00:33, 7 November 2018
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	[[File:Old_examples.jpg\|center]]		[[File:Old_examples.jpg\|center]]

			To better understand this, we could imagine in this way: E field makes positively charged particle to move along its path, as a positive particle, as it goes in direction of E Field, its potential of moving decrease. In another word, after the E field use its function (move the particle in a particular direction), the potential of it moving the particle decrease. And vice versa.

	== Harder Example ==		== Harder Example ==

Jruan34: /* Sign of Potential Difference */

2018-11-07T04:28:30Z

Sign of Potential Difference

← Older revision		Revision as of 00:28, 7 November 2018
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	For the last scenario it will be critical to have a strong understanding of the dot product and how to calculate it. ~~Remember that~~ a ~~dot product multiplies terms that~~ are in the '''~~same~~ direction''' ~~before being summed for a total~~. This means that when finding the dot product of two perpendicular vectors, the result will be '''zero'''. To better understand this, imagine the electric field between two very long capacitor plates. The electric field points from one plate to the other, let's say in the +x direction. If you wanted to move a charge at any location between the plates in either the +y or -y direction, your displacement vector would point in one of these directions. Whether you moved the particle +y or -y direction, the dot product of the electric field and displacement, and therefore the potential difference, will be zero.		For the last scenario, it will be critical to have a strong understanding of the dot product and how to calculate it. In a mathematical way, A·B = ABcos θ where θ is the angle between vector A and B. If A and B are in the same direction, '''θ = 0, cos θ = 1, then A·B = AB'''. If A and B are in opposite direction, '''θ = 180, cos θ = -1, then A·B = -AB'''. Last but not least, if A and B are perpendicular to each other, '''θ = 90, cos θ = 0, then A·B = 0'''. This means that when finding the dot product of two perpendicular vectors, the result will be '''zero'''.
			To better understand this, imagine the electric field between two very long capacitor plates. The electric field points from one plate to the other, let's say in the +x direction. If you wanted to move a charge at any location between the plates in either the +y or -y direction, your displacement vector would point in one of these directions. Whether you moved the particle +y or -y direction, the dot product of the electric field and displacement, and therefore the potential difference, will be zero.

	== Real Life Example to Explain Sign of Potential Difference ==		== Real Life Example to Explain Sign of Potential Difference ==

Jruan34 at 04:21, 7 November 2018

2018-11-07T04:21:14Z

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	== Quick Review of Delta symbol ==		== Quick Review of Delta symbol ==

	In the equation for the potential difference, we see a Delta for the path, also written as dL sometimes. This delta means a change in the path as taken from two different reference points. These reference points are known as '''initial and final''' or sometimes '''source and observation location'''. To properly calculate a delta or change, you must take the final and subtract the initial from it. More simply, '''Delta is Final-Initial'''. In doing problems with electrical field or magnetic field involving potential difference, the first step we usually do is to calculate r = pos_final - pos_initial. Then use it in several advanced formula: [[File:]]		In the equation for the potential difference, we see a Delta for the path, also written as dL sometimes. This delta means a change in the path as taken from two different reference points. These reference points are known as '''initial and final''' or sometimes '''source and observation location'''. To properly calculate a delta or change, you must take the final and subtract the initial from it. More simply, '''Delta is Final-Initial'''. In doing problems with electrical field or magnetic field involving potential difference, the first step we usually do is to calculate r = pos_final - pos_initial. Then use it in several advanced formula: [[File:Electric_field_formula.gif \|center]]

	Below are some practice problems to understand what dL would be.		Below are some practice problems to understand what dL would be.

Jruan34 at 04:15, 7 November 2018

2018-11-07T04:15:14Z

← Older revision		Revision as of 00:15, 7 November 2018
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	== Quick Review of Delta symbol ==		== Quick Review of Delta symbol ==

	In the equation for the potential difference, we see a Delta for the path, also written as dL sometimes. This delta means a change in the path as taken from two different reference points. These reference points are known as '''initial and final''' or sometimes '''source and observation location'''. To properly calculate a delta or change, you must take the final and subtract the initial from it. More simply, '''Delta is Final-Initial'''.		In the equation for the potential difference, we see a Delta for the path, also written as dL sometimes. This delta means a change in the path as taken from two different reference points. These reference points are known as '''initial and final''' or sometimes '''source and observation location'''. To properly calculate a delta or change, you must take the final and subtract the initial from it. More simply, '''Delta is Final-Initial'''. In doing problems with electrical field or magnetic field involving potential difference, the first step we usually do is to calculate r = pos_final - pos_initial. Then use it in several advanced formula: [[File:]]

	Below are some practice problems to understand what dL would be.		Below are some practice problems to understand what dL would be.

Jruan34 at 04:09, 7 November 2018

2018-11-07T04:09:44Z

← Older revision		Revision as of 00:09, 7 November 2018
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	[[File:Rsz 2212eq2.png\|center]]		[[File:Rsz 2212eq2.png\|center]]

	Consistent with previous convention, the delta symbol indicates "final - initial." We will use this same notation in showing the direction of the path. For example: Vb - Va ---> signifies the potential difference between location B (final) and location A (initial).		Consistent with the previous convention, the delta symbol (δ) indicates "final - initial." We will use this same notation in showing the direction of the path. For example δ V = Vb - Va ---> signifies the potential difference between location B (final) and location A (initial).


	For this equation, note that the result of the cross product between the electric field and displacement is negated before finding the potential difference. Furthermore, it is important to note that the electric field and displacement vectors are multiplied by the dot product. ~~Because of~~ this ~~dot product~~, we will analyze 3 different scenarios: path in the direction of the electric field, path in the ''opposite'' direction of the electric field, and the path moving ''perpendicular'' to the direction of the electric field.		For this equation, note that the result of the cross product between the electric field and displacement is negated before finding the potential difference. Furthermore, it is important to note that the electric field and displacement vectors are multiplied by the dot product. '''A · B = A * B * cosθ''' Due to this formula, we will analyze 3 different scenarios: path in the direction of the electric field(θ = 0°), path in the ''opposite'' direction of the electric field(θ = 180°), and the path moving ''perpendicular'' to the direction of the electric field(θ = 90°).

	== Quick Review of Delta symbol ==		== Quick Review of Delta symbol ==

	In the equation for potential difference, we see a Delta for the path, also written as dL sometimes. This delta means change in the path as taken from two different reference points. These reference points are known as '''initial and final''' or sometimes '''source and observation location'''. To properly calculate a delta, or change, you must take the final and subtract the initial from it. More simply, '''Delta is Final-Initial'''.		In the equation for the potential difference, we see a Delta for the path, also written as dL sometimes. This delta means a change in the path as taken from two different reference points. These reference points are known as '''initial and final''' or sometimes '''source and observation location'''. To properly calculate a delta or change, you must take the final and subtract the initial from it. More simply, '''Delta is Final-Initial'''.

	Below are some practice problems to understand what dL would be.		Below are some practice problems to understand what dL would be.

Jruan34 at 03:58, 7 November 2018

2018-11-07T03:58:00Z

← Older revision		Revision as of 23:58, 6 November 2018
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	== Introduction ==		== Introduction ==

	From previous sections, we know that the change in '''potential energy''' is equal to the charge multiplied by the change in '''potential difference'''(δU= q * δV). From Conservation of Energy(δV + δK = 0), the loss of kinetic energy must result in an increase in potential energy and vice versa in one same system. In another word, the change in the potential difference and kinetic energy can be positive ''or'' negative. For instance, when one object decreases its speed, its kinetic energy decreases. (δK < 0) Due to the conservation of energy, we can get δV > 0. However, we are mainly discussing the change of potential in electrical system as shown below:		From previous sections, we know that the change in '''potential energy''' is equal to the charge multiplied by the change in '''potential difference'''(δU = q * δV). From Conservation of Energy(δV + δK = 0), the loss of kinetic energy must result in an increase in potential energy and vice versa in one same system. In another word, the change in the potential difference and kinetic energy can be positive ''or'' negative. For instance, when one object decreases its speed, its kinetic energy decreases. (δK < 0) Due to the conservation of energy, we can get δV > 0. However, we are mainly discussing the change of potential in an electrical system as shown below:[[File:Rsz_2212eq1.png\|center]]
	[[File:Rsz_2212eq1.png\|center]]

	As seen from the equation above, two factors can affect the sign of potential energy. First, the charge of the particle being observed can be positive or negative (proton vs. electron). Second, and the topic of this page, the sign of the potential difference can also ~~affect~~ if a particle is gaining or losing potential energy.
			As seen from the equation above, two factors can affect the sign of potential energy. First, the charge of the particle being observed can be positive or negative (proton vs. electron). Second, and the topic of this page, the sign of the potential difference can also determine if a particle is gaining or losing potential energy.

	[[File:Potential one.jpg\|center]]		[[File:Potential one.jpg\|center]]

Jruan34 at 03:53, 7 November 2018

2018-11-07T03:53:21Z

← Older revision		Revision as of 23:53, 6 November 2018
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	CLAIMED BY ANDRES BEGAZO (Fall 2017)		CLAIMED BY ANDRES BEGAZO (Fall 2017), Junzhe Ruan(Fall 2018)


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	== Introduction ==		== Introduction ==

	~~Recall from~~ previous sections that the change in '''potential energy''' is equal to the charge multiplied by the change in '''potential difference'''. From Conservation of Energy, ~~we know that~~ an ''increase'' in potential energy ~~is related to a ''decrease'' in kinetic energy,~~ and vice versa. ~~Furthermore~~, ~~recall that~~ the change in ~~potential energy,~~ potential difference, kinetic energy~~, etc.~~ can be positive ''or'' negative. ~~The sign is important in calculating the potential~~ energy ~~because~~ the ~~Law~~ of ~~Energy Conservation states that~~ energy ~~cannot be created nor destroyed but rather transformed into a different kind (potential ----~~> ~~kinetic)~~.		From previous sections, we know that the change in '''potential energy''' is equal to the charge multiplied by the change in '''potential difference'''(δU= q * δV). From Conservation of Energy(δV + δK = 0), the loss of kinetic energy must result in an increase in potential energy and vice versa in one same system. In another word, the change in the potential difference and kinetic energy can be positive ''or'' negative. For instance, when one object decreases its speed, its kinetic energy decreases. (δK < 0) Due to the conservation of energy, we can get δV > 0. However, we are mainly discussing the change of potential in electrical system as shown below:

	[[File:Rsz_2212eq1.png\|center]]		[[File:Rsz_2212eq1.png\|center]]