Electric Potential Energy - AP Physics 2
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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.
There is an electric field of between two parallel plates of
Find the electric potential energy of a particle of charge
Use the equations for potential electric energy and electric potential:
Substitute.
Plug in known values and solve.
Use the equations for potential electric energy and electric potential:
Substitute.
Plug in known values and solve.
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electrons pass through a 
resistor in 11 minutes. What is the potential difference across that resistor?
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.
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
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
Now that we have the current, we can use Ohm's Law to find the voltage.
Therefore, the potential difference is 2.96V.
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What is the electric potential between two terminals of a cell if it requires 
of work to transfer 
between the terminals?
What is the electric potential between two terminals of a cell if it requires
Write the formula for the potential difference.
Substitute the work and charge. The unit is in volts.
Write the formula for the potential difference.
Substitute the work and charge. The unit is in volts.
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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?
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?
Electric field strength is the slope of the electric potential:
Remember to convert into SI units (meters):
Electric field strength is the slope of the electric potential:
Remember to convert into SI units (meters):
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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?
In a region of space, there is an electric field whose magnitude is
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
This problem is solved using the work-kinetic energy theory:
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
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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?
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
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:
In order to solve for electrical potential energy, we'll need to remember the equation for it.
In the above expression,
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:
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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?
Suppose that a positively charged particle of
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:
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
Plugging in the values we have, we can obtain our answer:
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Determine the electric potential energy of a 
charge in an electric potential of 
.
Determine the electric potential energy of a
Converting units:
Use the equation for electric potential energy:
Converting units:
Use the equation for electric potential energy:
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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.
An electron is placed in an electric potential of
Conservation of energy:
Assuming no external work done
Electric potential energy:
Solving for velocity:
Plugging in values:
Conservation of energy:
Assuming no external work done
Electric potential energy:
Solving for velocity:
Plugging in values:
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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.
A helium nucleus is placed in an electric potential of
Conservation of energy:
Assuming no external work done
Electric potential energy:
Solving for velocity:
Plugging in values:
Conservation of energy:
Assuming no external work done
Electric potential energy:
Solving for velocity:
Plugging in values:
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A proton is placed into an electric potential of 
, determine the final velocity after it is released.
A proton is placed into an electric potential of
Conservation of energy:
Assuming no external work done
Electric potential energy:
Solving for velocity:
Plugging in values:
Conservation of energy:
Assuming no external work done
Electric potential energy:
Solving for velocity:
Plugging in values:
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A 
car is traveling at 
. It is carrying a 
charge against an electric field of 
. Determine how far the car will travel before stopping.
A
Force in an electric field:
Using conservation of energy, assuming no external work on system:
Definition of electric potential energy:
Definition of electric potential:
Combining equations:
Assuming final velocity is zero:
is the distance traveled
Converting 
to 
Plugging in values:
Solving for 
Force in an electric field:
Using conservation of energy, assuming no external work on system:
Definition of electric potential energy:
Definition of electric potential:
Combining equations:
Assuming final velocity is zero:
Converting
Plugging in values:
Solving for
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A ball of mass 
with 
missing electrons is accelerated with a 
electric field. Determine the final velocity.
A ball of mass
Force in an electric field:
Using conservation of energy, assuming no external work on system:
Definition of electric potential energy:
Combining equations:
Assuming initial velocity and final electric potential is zero:
The charge, 
will be equal to the electron charge time the number of electrons missing, 
Converting 
to 
and plugging in values:
Force in an electric field:
Using conservation of energy, assuming no external work on system:
Definition of electric potential energy:
Combining equations:
Assuming initial velocity and final electric potential is zero:
The charge,
Converting
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If a 
charged particle moves a distance of 
within a 
electric field, what is the magnitude of change in this particle's electrical potential energy?
If a
In this question, we're given the charge of a particle, the distance that it travels, and the electric field within which this movement occurs. We're asked to find the magnitude of the change in electrical potential energy that this particle undergoes.
We can begin this problem by writing an expression for the electric potential energy.
Since we have the particle's charge, but not its electric potential, we need to find a way to obtain this term. To do this, we can make use of the distance the particle travels, as well as the electric field.
Combining these expressions, we can obtain our answer.
In this question, we're given the charge of a particle, the distance that it travels, and the electric field within which this movement occurs. We're asked to find the magnitude of the change in electrical potential energy that this particle undergoes.
We can begin this problem by writing an expression for the electric potential energy.
Since we have the particle's charge, but not its electric potential, we need to find a way to obtain this term. To do this, we can make use of the distance the particle travels, as well as the electric field.
Combining these expressions, we can obtain our answer.
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