Electric Potential Energy and Electric Potential (Dynamic Study)

If an object with charge +2 nC moves from a location that has a potential of 20 V to a location with a potential of -10 V, what has happened to the potential energy of the system?

If an object with charge +2 nC moves from a location that has a potential of 20 V to a location with a potential of -10 V, the potential energy of the system has decreased by (SEE IMAGE).

If an electron is moved in a direction perpendicular to an equipotential surface, ______.

it will be moving either in the same or exactly opposite direction as the electric field at that location

Consider two point charges, A and B, separated by a distance, d. How would we find the total electric potential energy of this arrangement?

To calculate the total electric potential energy of two point charges, A and B, separated by a distance, d, we would calculate one electric potential energy for the pair. Potential energy (of any kind) is a property of a system and cannot be calculated for a single object by itself. Nor is energy (of any kind) something that can be "applied".

When an electron approaches a positively charged nucleus, ______.

When an electron approaches a positively charged nucleus, the electric potential energy of the system decreases while the potential at the electron's location increases. Electric potential energy is a property of the system, so we look at the interaction between the nucleus and the electron.

Which of these is a good description of the difference between electric potential energy and electric potential?

An important difference between electric potential energy and electric potential is that electric potential energy is a property of a system of multiple charges, while electric potential is a property of a location in space near a charge distribution. The two concepts are intimately connected, but the electric potential is a property of a certain location in space, whether there happens to be a charged object at that location or not. Electric potential energy, on the other hand, is only something that can be calculated as a property of a system of charged objects interacting with each other.

As we consider various points that are all on the same equipotential surface near some distribution of charge, ______.

As we consider various points that are all on the same equipotential surface near some distribution of charge, the electric potential is the same at every point, but the electric potential energy is different at every point. Electric potential is a property of space and does not require that there be any object at that location in space. By definition, the electric potential is the same at all points on a given equipotential surface. Electric potential energy, on the other hand, is a property of a system of multiple objects and can only be calculated if there is an actual charged object at that location. Thus, it doesn't even make sense to talk about the electric potential energy at various points in space.

As we consider various points that are all on the same equipotential surface near some distribution of charge, ______

As we consider various points that are all on the same equipotential surface near some distribution of charge, the electric potential is the same at every point. Electric potential is a property of space and does not require that there be any object at that location in space. By definition, the electric potential is the same at all points on a given equipotential surface. Electric potential energy, on the other hand, is a property of a system of multiple objects and can only be calculated if there is an actual charged object at that location.

How are electric field lines related to equipotential surfaces?

Electric field lines are always perpendicular to equipotential surfaces and point toward locations of lower potential. If the electric field had any component that pointed along the equipotential surface, the potential would not be the same as you moved in that direction along the equipotential surface, which is a contradiction. Electric field lines point in the direction along which the potential is changing the fastest (known as the gradient of the potential) and they always point in the direction a positive charge would be pushed, which is from higher electric potential to lower electric potential.

Every point on an equipotential surface ______.

Every point on an equipotential surface has the same electric potential. As the name implies, an equipotential surface is a three-dimensional surface defined by a set of points that all have the same electric potential. These points will, in general, have differing electric fields, both in magnitude and direction.

If a proton is moved a certain distance directly opposite an external electric field, what can we say about the change in the electric potential it experiences?

If a proton is moved a certain distance directly opposite an external electric field, the electric potential it experiences will increase. Electric field lines point in the direction a positive charge would be pushed by the electric force. This means they always push from locations with higher electric potential toward locations with lower electric potential. So as long as the proton is moving opposite the external electric field, the proton will experience larger and larger electric potentials. Notice that the charge of the proton is irrelevant to this result.

If an electron is moved a certain distance directly opposite an external electric field, what can we say about the change in the electric potential energy of the system?

If an electron is moved a certain distance directly opposite an external electric field, the electric potential energy of the system will decrease. Electric field lines point in the direction a positive charge would be pushed by the electric force. This means they always push from locations with higher electric potential toward locations with lower electric potential.

If an electron is moved a certain distance directly opposite an external electric field, what can we say about the change in the electric potential energy of the system?

If an electron is moved a certain distance directly opposite an external electric field, the electric potential energy of the system will decrease. Electric field lines point in the direction a positive charge would be pushed by the electric force. This means they always push from locations with higher electric potential toward locations with lower electric potential. Since the electron is negatively charged, the increasing electric potential means a loss in electric potential energy.

If an electron is moved in a direction perpendicular to an equipotential surface, ______.

If an electron moves in a direction perpendicular to an equipotential surface the potential it experiences must change. By definition, an equipotential surface defines those points that all have the same potential. So moving away from this surface means the electric potential it experiences must change. In fact, by moving perpendicular to the surface, the potential will change faster than it would in any other direction.

If an electron moves in a direction perpendicular to an equipotential surface, ______.

If an electron moves in a direction perpendicular to an equipotential surface the potential it experiences must change. By definition, an equipotential surface defines those points that all have the same potential. So moving away from this surface means the electric potential it experiences must change. In fact, by moving perpendicular to the surface, the potential will change faster than it would in any other direction.

If an object with charge -3 nC moves from a location that has a potential of -20 V to a location with a potential of -10 V, what has happened to the potential energy of the system?

If an object with charge -3 nC moves from a location that has a potential of -20 V to a location with a potential of -10 V, the potential energy of the system has decreased by (see image)

If there is a system with two electrons and a proton, can the electric potential energy of the system be exactly zero?

In a system of two electrons the electric potential energy could be zero if they were arranged properly. Electric potential energy is a scalar quantity, calculated for a given arrangement of charges. The energy between two point charges can be calculated using (see image) . If the three objects are arranged properly the total electric potential energy would have two negative terms and one positive term, which would all add up to zero.

If there is a system with a proton and an electron, can the electric potential energy of the system be exactly zero?

In a system with a proton and an electron the electric potential energy will be negative no matter how they are arranged. Electric potential energy is a scalar quantity, calculated for a given arrangement of charges. The energy between two point charges can be calculated using . We can see that for a positively charged object interacting with a negatively charged object (such as the proton and electron), the electric potential energy will always be negative.

If there is a system with two electrons, can the electric potential energy of the system be exactly zero?

In a system with two electrons the electric potential energy will be positive no matter how they are arranged. Electric potential energy is a scalar quantity, calculated for a given arrangement of charges. The energy between two point charges can be calculated using (see image). We can see that for any two negatively charged objects (such as the two electrons), the electric potential energy will always be positive.

Which of the following is a good description of the electric force between stationary charged objects?

The electric force between stationary charged objects is a conservative force for which there is a corresponding potential energy. A conservative force is one for which the work done by the force is path-independent. The electric force between stationary charged objects is a conservative force and therefore has a potential energy associated with it.

Consider a point 1 cm away from an electron with nothing else nearby. What expression could represent the electric potential at that location?

The electric potential at a point 1 cm away from an electron could be represented by (see image) . Using the definition for the potential due to a single point charge, we simply include the sign and charge of the electron and the distance in the denominator.

Consider three point charges, A, B, and C, arranged in an equilateral triangle, with distance d on each side. How would we find the total electric potential energy of this arrangement?

To calculate the total electric potential energy of three point charges, A, B, and C, arranged in an equilateral triangle, with distance d on each side, we would find the three electric potential energies (one for each pair) and add them up. Potential energy (of any kind) is a property of a system and cannot be calculated for a single object by itself. Nor is energy (of any kind) something that can be "applied".

A cube of copper and a sphere of aluminum are both positively charged and connected by a wire. What do the two conductors have in common?

When a cube of copper and a sphere of aluminum are both positively charged and connected by a wire, they both have the same electric potential. Within a continuous conductor (even if there are different metals involved) the electric potential must be the same everywhere. If there were some location where the potential were lower (or higher), charges would be driven toward (or away) from that location until the potential evened out. The two objects will not have the same electric field at their surfaces (or nearby) because the electric field depends on their size, shape, and total charge. The two objects will not have the same net charge. For example, a smaller charged object and a larger charged object must have different net charges in order to have equal electric potentials.

An arbitrarily shaped piece of conductor is given a net negative charge and is alone in space. What can we say about the electric potential within the conductor? Assume that the electric potential is zero at points that are very far away from the conductor.

When an arbitrarily shaped piece of conductor is given a net negative charge and is alone in space, the electric potential in the conductor will be negative and constant throughout the conductor. The charges in a conductor are free to move around, resulting in equal electric potential everywhere inside the conductor. If some locations had a higher or lower electric potential, the charges would move in response and would thereby correct the imbalance. In addition, given that the electric potential is zero very far from the conductor, the potential must be negative as we approach the conductor. So the potential starts at zero (very far away), becomes more and more negative as we approach the conductor, and then becomes constant (still negative) as we go into the conductor.

An arbitrarily shaped piece of conductor is given a net positive charge and is alone in space. What can we say about the electric potential within the conductor? Assume that the electric potential is zero at points that are very far away from the conductor.

When an arbitrarily shaped piece of conductor is given a net negative charge and is alone in space, the electric potential in the conductor will be positive and constant throughout the conductor. The charges in a conductor are free to move around, resulting in equal electric potential everywhere inside the conductor. If some locations had a higher or lower electric potential, the charges would move in response and would thereby correct the imbalance. In addition, given that the electric potential is zero very far from the conductor, the potential must be positive as we approach the conductor. So the potential starts at zero (very far away), becomes more and more positive as we approach the conductor, and then becomes constant (still positive) as we go into the conductor.

When two electrons are 1 cm apart, what expression could represent their electric potential energy?

When two electrons are 1 cm apart, their electric potential energy could be represented by (SEE IMAGE). Using the definition of the potential energy for two point charges with the charges replaced by electron charges (both negative) and the distance between them in the denominator, the potential energy will end up positive.