Physics Book - User contributions [en]

Sign of a Potential Difference

2016-11-28T01:23:57Z

Damador3: /* Examples */

CLAIMED BY DYLAN AMADOR (FALL '16)

----
This article covers the sign of potential difference, and how to determine the sign in different situations involving a particle and an electric field.

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.
[[File:PotEnergy&Diff_eq.jpg]]
In this article we will see how the change in potential energy can be positive, negative, or zero and then we will be able to look back and see how the sign of this change relates to the potential energy, kinetic energy, and so on.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:Examples.jpg]]
**because of site formatting this image is unable to be viewed in its original format
*To view the image in the upright orientation follow this link: https://drive.google.com/open?id=0BxZ16KwNznRoaXV4a25TMmJVUEU

== Summary ==
When determining the sign of the potential difference, there will be 3 different scenarios that will determine whether the sign of the potential difference is positive, negative, or zero. Pay close attention to notation when considering the change in a quantity (potential, displacement, etc..) in order to avoid confusing the wrong sign. Attention to detail when find the sign of potential difference will make solving the more difficult problems at the end of the chapter a little easier. The following summary of the 3 scenarios is extremely helpful:

Path going in direction of ''E'' ------> Potential is '''decreasing'''

Path going opposite to ''E'' -------> Potential is '''increasing'''

Path perpendicular to ''E'' --------> Potential '''does not change'''

Sign of a Potential Difference

2016-11-28T01:14:18Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----
This article covers the sign of potential difference, and how to determine the sign in different situations involving a particle and an electric field.

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.
[[File:PotEnergy&Diff_eq.jpg]]
In this article we will see how the change in potential energy can be positive, negative, or zero and then we will be able to look back and see how the sign of this change relates to the potential energy, kinetic energy, and so on.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:Examples.jpg]]

== Summary ==
When determining the sign of the potential difference, there will be 3 different scenarios that will determine whether the sign of the potential difference is positive, negative, or zero. Pay close attention to notation when considering the change in a quantity (potential, displacement, etc..) in order to avoid confusing the wrong sign. Attention to detail when find the sign of potential difference will make solving the more difficult problems at the end of the chapter a little easier. The following summary of the 3 scenarios is extremely helpful:

Path going in direction of ''E'' ------> Potential is '''decreasing'''

Path going opposite to ''E'' -------> Potential is '''increasing'''

Path perpendicular to ''E'' --------> Potential '''does not change'''

Sign of a Potential Difference

2016-11-28T01:08:58Z

Damador3: /* Summary */

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.
[[File:PotEnergy&Diff_eq.jpg]]

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:Examples.jpg]]

== Summary ==
When determining the sign of the potential difference, there will be 3 different scenarios that will determine whether the sign of the potential difference is positive, negative, or zero. Pay close attention to notation when considering the change in a quantity (potential, displacement, etc..) in order to avoid confusing the wrong sign. Attention to detail when find the sign of potential difference will make solving the more difficult problems at the end of the chapter a little easier. The following summary of the 3 scenarios is extremely helpful:

Path going in direction of ''E'' ------> Potential is '''decreasing'''

Path going opposite to ''E'' -------> Potential is '''increasing'''

Path perpendicular to ''E'' --------> Potential '''does not change'''

Sign of a Potential Difference

2016-11-28T01:08:32Z

Damador3: /* Summary */

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.
[[File:PotEnergy&Diff_eq.jpg]]

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:Examples.jpg]]

== Summary ==
When determining the sign of the potential difference, there will be 3 different scenarios that will determine whether the sign of the potential difference is positive, negative, or zero. Pay close attention to notation when considering the change in a quantity (potential, displacement, etc..) in order to avoid confusing the wrong sign. Attention to detail when find the sign of potential difference will make solving the more difficult problems at the end of the chapter a little easier. The following summary of the 3 scenarios is extremely helpful:

Path going in direction of ''E'' ------> Potential is '''decreasing'''

Path going opposite to '''E''' -------> Potential is '''increasing'''

Path perpendicular to '''E''' --------> Potential '''does not change'''

Sign of a Potential Difference

2016-11-28T00:53:51Z

Damador3: /* Summary */

Sign of a Potential Difference

2016-11-28T00:10:40Z

Damador3:

Sign of a Potential Difference

2016-11-28T00:00:06Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.
[[File:PotEnergy&Diff_eq.jpg]]

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:PotDiffExamples.jpg]]

== Summary ==
When determining the sign of

Sign of a Potential Difference

2016-11-27T23:59:55Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.
[[File:PotEnergy&Diff_eq.jpg]]

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:PotExamples.jpg]]

== Summary ==
When determining the sign of

File:PotSignExamples.jpg

2016-11-27T23:59:25Z

Damador3: 3 scenario examples to determine the sign of the potential difference.

3 scenario examples to determine the sign of the potential difference.

Sign of a Potential Difference

2016-11-27T23:58:01Z

Damador3:

Sign of a Potential Difference

2016-11-27T23:56:20Z

Damador3: /* Direction of Path vs. Direction of Electric Field */

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:PotentialDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==

== Summary ==
When determining the sign of

Sign of a Potential Difference

2016-11-27T23:55:12Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
[[File:potDiff_efield_eq.jpg]]
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==

== Summary ==
When determining the sign of

File:PotentialDiff efield eq.jpg

2016-11-27T23:53:54Z

Damador3: Image of the equation relation potential difference with electric field and displacement.

Image of the equation relation potential difference with electric field and displacement.

File:Examples.jpg

2016-11-27T23:52:23Z

Damador3: Example Problems for the 3 Sign Scenarios

Example Problems for the 3 Sign Scenarios

Sign of a Potential Difference

2016-11-27T23:52:00Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==

== Summary ==
When determining the sign of

File:PotEnergy&Diff eq.jpg

2016-11-27T23:49:49Z

Damador3: Picture showing the equation relating potential energy with potential difference and charge.

Picture showing the equation relating potential energy with potential difference and charge.

Sign of a Potential Difference

2016-11-27T23:48:47Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==
[[File:examples.jpg]]

== Summary ==
When determining the sign of

Sign of a Potential Difference

2016-11-27T23:28:02Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Examples ==

== Summary ==
When determining the sign of

Sign of a Potential Difference

2016-11-27T23:10:25Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)

----

== Introduction ==

Recall from previous sections that the change in '''potential energy''' is equal to the charge times 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.

== Direction of Path vs. Direction of Electric Field ==

From the equation relating potential difference with electric field and motion, we can see that the sign of the potential difference is dependent on the direction of both the electric field and displacement vectors.
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.

(1) Same Direction
In this scenario, the dot product yields a positive result, so when multiplied by the negative term in the equation, the resulting potential difference will be '''negative'''.

(2) Opposite Direction
When the electric field and displacement are in opposite directions, the result of the dot product will be negative which leads to a '''positive potential difference''' after multiplying that result by -1.

(3) Directions are Perpendicular
For this 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 will be zero.
Moving forward with the concept of potential difference, this concept will be useful to remember for solving problems.

== Indicating Path Direction (sign convention) ==

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).

== Summary ==
When determining the sign of

Sign of a Potential Difference

2016-11-27T21:56:38Z

Damador3:

Sign of a Potential Difference

2016-11-27T00:12:24Z

Damador3:

CLAIMED BY DYLAN AMADOR (FALL '16)