Electric Potential Energy: Potential Difference Quiz

PDF page 896: a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly. We use the letters PE to denote electric potential energy, which has units of joules (J). The change in potential energy, , is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, . For example, work done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative . There must be a minus sign in front of to make positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point.

PDF page 896: a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly. We use the letters PE to denote electric potential energy, which has units of joules (J). The change in potential energy, , is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, . For example, work done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative . There must be a minus sign in front of to make positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point.

PDF page 895: When a free positive charge is accelerated by an electric field, such as shown in Figure 19.2, it is given kinetic energy. The process is analogous to an object being accelerated by a gravitational field. It is as if the charge is going down an electrical hill where its electric potential energy is converted to kinetic energy. Let us explore the work done on a charge by the electric field in this process, so that we may develop a definition of electric potential energy.

PDF page 895: to another form. Work is done by a force, but since this force is conservative, we can write . The electrostatic or Coulomb force is conservative, which means that the work done on is independent of the path taken. This is exactly analogous to the gravitational force in the absence of dissipative forces such as friction. When

PDF page 896: a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy (because it depends only on position) than to calculate the work directly. We use the letters PE to denote electric potential energy, which has units of joules (J). The change in potential energy, , is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, . For example, work done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative . There must be a minus sign in front of to make positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point.

PDF page 895: to another form. Work is done by a force, but since this force is conservative, we can write . The electrostatic or Coulomb force is conservative, which means that the work done on is independent of the path taken. This is exactly analogous to the gravitational force in the absence of dissipative forces such as friction. When

PDF page 896: Gravitational potential energy and electric potential energy are quite analogous. Potential energy accounts for work done by a conservative force and gives added insight regarding energy and energy transformation without the necessity of dealing with the force directly. It is much more common, for example, to use the concept of voltage (related to electric potential energy) than to deal with the Coulomb force directly. Calculating the work directly is generally difficult, since and the direction and magnitude of can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that, since , the work, and hence , is proportional to the test charge To have a physical quantity that is independent of test charge, we define electric potential (or simply potential, since electric is understood) to be the potential energy per unit charge:

PDF page 896: This is the electric potential energy per unit charge.

PDF page 896: The potential difference between points A and B, , is thus defined to be the change in potential energy of a charge moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

PDF page 896: The potential difference between points A and B, , is thus defined to be the change in potential energy of a charge moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

PDF page 896: The potential difference between points A and B, , is thus defined to be the change in potential energy of a charge moved from A to B, divided by the charge. Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.

PDF page 897: The familiar term voltage is the common name for potential difference. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. For example, every battery has two terminals, and its voltage is the potential difference between them. More fundamentally, the point you choose to be zero volts is arbitrary. This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor. In summary, the relationship between potential difference (or voltage) and electrical potential energy is given by

PDF page 897: Voltage is not the same as energy. Voltage is the energy per unit charge. Thus a motorcycle battery and a car battery can both have the same voltage (more precisely, the same potential difference between battery terminals), yet one stores much more energy than the other since . The car battery can move more charge than the motorcycle battery, although both are 12 V batteries.