# AP Physics 2 : Electric Potential Energy

## Example Questions

### Example Question #1 : Electric Potential Energy

electrons pass through a  resistor in 11 minutes. What is the potential difference across that resistor?

Explanation:

We need to find the voltage, and we have the resistance, so if we can find the current, then we can use Ohm's Law to find the voltage.

The definition of current is amount of charge that flows through a point in  time, so current can be calculated using this equation:

We're told how many electrons have passed through a resistor, and we know how much charge a single electron has. If we convert the number of electrons into total amount of charge, we can divide that number by the amount of time in seconds to find the current.

Now we have the amount of charge in  and the amount of time in seconds, so we divide the two.

Now that we have the current, we can use Ohm's Law to find the voltage.

Therefore, the potential difference is 2.96V.

### Example Question #2 : Electric Potential Energy

What is the electric potential between two terminals of a cell if it requires  of work to transfer  between the terminals?

Explanation:

Write the formula for the potential difference.

Substitute the work and charge. The unit is in volts.

### Example Question #1 : Electric Potential Energy

There is an electric field of  between two parallel plates of . The two plates are  apart.

Find the electric potential energy of a particle of charge  placed right at the surface of the positive plate.

None of these

Explanation:

Use the equations for potential electric energy and electric potential:

Substitute.

Plug in known values and solve.

### Example Question #71 : Electrostatics

A student is working on a laboratory exercise in which she measures the electric potential (voltage) at several points in an electric field. Before graphing the potential isolines, she measures the electric potential to be 3V at one point in the field and 7V at a point 3cm from the first point. What is the average electric field strength between the two points the student measured?

Explanation:

Electric field strength is the slope of the electric potential:

Remember to convert into SI units (meters):

### Example Question #71 : Electrostatics

In a region of space, there is an electric field whose magnitude is  pointing due North. An electron enters this field traveling due North with an initial velocity . It enters the field at point A, where the electric potential is 1.5V. As it travels 2cm in the field to point B, the potential changes to 0V. What will the electron's velocity be when it arrives at point B?

Cannot be determined

Explanation:

This problem is solved using the work-kinetic energy theory: . In an electric field, work is equal to charge times change in potential:

Since an electron has a negative charge, decreasing potential increases its kinetic energy, the opposite of what would happen to a proton with its positive charge. Combine these equations:

Plug in known values and solve

### Example Question #6 : Electric Potential Energy

Suppose that a point charge of 1 Coulomb undergoes a change in which it is moved from point A to point B while in the presence of an external electric field. During this transposition, it undergoes a voltage change of . What change in electrical potential energy occurs in this scenario?

Explanation:

In order to solve for electrical potential energy, we'll need to remember the equation for it.

In the above expression,  represents electrical potential energy,  and  represent different point charges, and  represents the distance between their centers. In this example, one of these charges will be the source of the external electric field, while the other charge will be the one that is undergoing a transposition from point A to point B.

Furthermore, we can remember the equation for voltage:

With both these equations in mind, we can combine the two:

This above expression tells us that the electrical potential energy of a system is directly proportional to the voltage change and to the charge of the test charge that is undergoing the voltage change.

Plug in the values and solve for electrical potential energy:

### Example Question #781 : Ap Physics 2

Suppose that a positively charged particle of  moves from position A to position B along a curved path that is  long, as shown in the figure. Within this region, there is an electric field of  oriented from right to left. If the particle undergoes a net displacement of , how much work is required to move this particle?

There is not enough information to answer this question.

Explanation:

For this question, we're presented with a situation in which a positively charged particle is traveling through an electric field along a defined path. We're then asked to determine the amount of energy we need to input in order to make this process occur.

We'll need to use an equation that relates charge, electric field, and energy, which we can derive as follows.

Next, we need to make sure to use the correct value for distance. Since we know that the electric force is a conservative force, we know that the movement of the particle from A to B is independent of the path taken. In other words, for a conservative force, the only thing that matters is the initial state and the final state. Also, since the electric field is oriented horizontally from right to left, we only care about the movement of the particle along the horizontal direction. Thus, we do not use the  value (distance of path taken), but instead we use the  value (net distance traveled along the electric field).

Plugging in the values we have, we can obtain our answer:

### Example Question #1 : Electric Potential Energy

Determine the electric potential energy of a  charge in an electric potential of .

None of these

Explanation:

Converting units:

Use the equation for electric potential energy:

### Example Question #9 : Electric Potential Energy

An electron is placed in an electric potential of , determine the velocity of the electron after passing through the potential, assuming it was motionless at the beginning.

None of these

Explanation:

Conservation of energy:

Assuming no external work done

Electric potential energy:

Solving for velocity:

Plugging in values:

### Example Question #10 : Electric Potential Energy

A helium nucleus is placed in an electric potential of , determine the velocity of the helium nucleus after passing through the potential, assuming it was motionless at the beginning.

None of these

Explanation:

Conservation of energy:

Assuming no external work done

Electric potential energy:

Solving for velocity:

Plugging in values: