Electrostatics - AP Physics 1
Card 1 of 144
An excess charge of 
is put on an ideal neutral conducting sphere with radius 
. What is the Coulomb force this excess charge exerts on a point charge of 
that is 
from the surface of the sphere?
An excess charge of
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Two principal realizations help with solving this problem, both derived from Gauss’ law for electricity:
-
The excess charge on an ideal conducting sphere is uniformly distributed over its surface
-
A uniform shell of charge acts, in terms of electric force, as if all the charge were contained in a point charge at the sphere’s center
With these realizations, an application of Coulomb’s law answers the question. If 
is the point charge outside the sphere, then the force 
on 
is:
In this equation, 
is Coulomb’s constant, 
is the excess charge on the spherical conductor, and 
is total distance in meters of 
from the center of the conducting sphere.
Using the given values in this equation, we can calculate the generated force:
Two principal realizations help with solving this problem, both derived from Gauss’ law for electricity:
-
The excess charge on an ideal conducting sphere is uniformly distributed over its surface
-
A uniform shell of charge acts, in terms of electric force, as if all the charge were contained in a point charge at the sphere’s center
With these realizations, an application of Coulomb’s law answers the question. If
In this equation,
Using the given values in this equation, we can calculate the generated force:
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Charges A and B are placed a distance of 
from one another. The charge of particle A is 
whereas the charge of particle B is 
. Charge B experiences an electrostatic force of 
from charge A. Similarly, charge A experiences an electrostatic force of 
from charge B.
What is the ratio of 
to 
?
Charges A and B are placed a distance of
What is the ratio of
Tap to reveal answer
This question is very simple if you realize that the force experienced by both charges is equal.
The definition of the two electrostatic forces are given by Coulomb's law:
In this question, we can rewrite this equation in terms of our given system.
It doesn’t matter if the charges of the two particles are different; both particles experience the same force because the charges of both particles are accounted for in the electrostatic force equation (Coulomb's law). This conclusion can also be made by considering Newton's third law: the force of the first particle on the second will be equal and opposite the force of the second particle on the first.
Since the forces are equal, their ratio will be 
.
This question is very simple if you realize that the force experienced by both charges is equal.
The definition of the two electrostatic forces are given by Coulomb's law:
In this question, we can rewrite this equation in terms of our given system.
It doesn’t matter if the charges of the two particles are different; both particles experience the same force because the charges of both particles are accounted for in the electrostatic force equation (Coulomb's law). This conclusion can also be made by considering Newton's third law: the force of the first particle on the second will be equal and opposite the force of the second particle on the first.
Since the forces are equal, their ratio will be
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If the distance between two charged particles is doubled, the strength of the electric force between them will .
If the distance between two charged particles is doubled, the strength of the electric force between them will .
Tap to reveal answer
Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:
The strength of the force will be inversely proportional to the square of the distance between the charges.
When the distance between the charges is doubled, the total force will be divided by four (quartered).
Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:
The strength of the force will be inversely proportional to the square of the distance between the charges.
When the distance between the charges is doubled, the total force will be divided by four (quartered).
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Two protons are on either side of an electron as shown below:
The electron is 30 µm away from the proton on its left and 10 µm away from the proton on its right. What is the magnitude and direction of the net electric force acting on the electron?
A proton has a charge of 
Two protons are on either side of an electron as shown below:
The electron is 30 µm away from the proton on its left and 10 µm away from the proton on its right. What is the magnitude and direction of the net electric force acting on the electron?
A proton has a charge of
Tap to reveal answer
The net force on the electron is the sum of the forces between the electron and each of the protons:
These forces are given by Coulomb's law:
Using the numbers given, we get:
Because opposite charges attract, 
points left (the negative direction) and 
points right (the positive direction).
Therefore, the net force is
Because this value is positive, the direction is rightward.
The net force on the electron is the sum of the forces between the electron and each of the protons:
These forces are given by Coulomb's law:
Using the numbers given, we get:
Because opposite charges attract,
Therefore, the net force is
Because this value is positive, the direction is rightward.
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If we have 2 charges, 
and 
, that are 
apart, what is the magnitude of the force exerted on 
by 
if we know that 
has a charge of 
and 
has a charge of 
?
If we have 2 charges,
Tap to reveal answer
Use Coulomb's Law
Plug in known values and solve.
A negative value for electric force indicates an attractive force. This makes sense since our two charges have opposite signs. Since we're asked for magnitude, all answer choices are positive.
Use Coulomb's Law
Plug in known values and solve.
A negative value for electric force indicates an attractive force. This makes sense since our two charges have opposite signs. Since we're asked for magnitude, all answer choices are positive.
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If we have 2 charges, 
and 
, that are 
apart, what is the force exerted on 
by 
if we know that 
has a charge of 
and 
has a charge of 
?
If we have 2 charges,
Tap to reveal answer
Use Coulomb's law.
Plug in known values and solve.
Note that the force between two charges of the same sign (both positive or both negative) is positive. This indicates the force is repulsive, which makes sense since both charges are positive.
Use Coulomb's law.
Plug in known values and solve.
Note that the force between two charges of the same sign (both positive or both negative) is positive. This indicates the force is repulsive, which makes sense since both charges are positive.
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If we have 2 charges, 
and 
, that are 
apart, what is the force exerted on 
by 
if we know that 
has a charge of 
and 
has a charge of 
?
If we have 2 charges,
Tap to reveal answer
Use Coulomb's law.
Plug in known values and solve.
Note that this force is positive, which means it's repulsive.
Use Coulomb's law.
Plug in known values and solve.
Note that this force is positive, which means it's repulsive.
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If we have 2 charges, 
and 
, that are 
apart, what is the force exerted on 
by 
if we know that 
has a charge of 
and 
has a charge of 
?
If we have 2 charges,
Tap to reveal answer
Use Coulomb's law.
Plug in known values and solve.
Note that this force is positive, which means that it's repulsive.
Use Coulomb's law.
Plug in known values and solve.
Note that this force is positive, which means that it's repulsive.
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Two point charges, 
and 
are separated by a distance of 
. What is the force of repulsion between them?
Two point charges,
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The force of attraction/repulsion between two point charges is given by Coulomb's Law:
If the charges are of like sign, then there well be a repulsive force between the two. Alternatively, if the net force is positive, it is repulsive; if it is negative, it is attractive.
Therefore, the force of repulsion between the two charges is:
The force of attraction/repulsion between two point charges is given by Coulomb's Law:
If the charges are of like sign, then there well be a repulsive force between the two. Alternatively, if the net force is positive, it is repulsive; if it is negative, it is attractive.
Therefore, the force of repulsion between the two charges is:
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Two point charges, 
and 
are separated by a distance of 
. What is the work required to move them closer together to a distance of 
?
Two point charges,
Tap to reveal answer
The force of attraction/repulsion between two point charges is given by Coulomb's Law:
If the charges are of like sign, then there well be a repulsive force between the two.
Work is given as the dot product of force and distance. However, in this case, force is also dependent on distance.
The amount of work required to move a charge an incremental distance, 
, is given as:
The negative sign in this case is to account for repulsion.
The total work to change distances between charges can then be found by taking the integral with respect to distance:
Since 
are constants, they can be factored out of the integral:
The force of attraction/repulsion between two point charges is given by Coulomb's Law:
If the charges are of like sign, then there well be a repulsive force between the two.
Work is given as the dot product of force and distance. However, in this case, force is also dependent on distance.
The amount of work required to move a charge an incremental distance,
The negative sign in this case is to account for repulsion.
The total work to change distances between charges can then be found by taking the integral with respect to distance:
Since
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Write, in vector notation, the force exerted on a positive charge of 
by a negative charge of 
, if the two charges sitting on the 
-axis, with the positive charge sitting 
to the right of the negative charge?
Write, in vector notation, the force exerted on a positive charge of
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Coulomb's law in vector notation is given as:
, where 
is Coulomb's constant, 
and 
are the two charges, 
is the distance between the charges squared, and 
is the unit vector going from one charge to another.
To write this in vector notation, we have to know the unit vector going from the negative to the positive charge, since we're trying to determine the force on the positive charge. Since they are both sitting on the 
-axis, with the negative charge to the left of the positive, the unit vector will be going in the direction of positive 
:
We know that 
We know that 
, 
, and 
. Putting this together:
We can rewrite this as:
Coulomb's law in vector notation is given as:
To write this in vector notation, we have to know the unit vector going from the negative to the positive charge, since we're trying to determine the force on the positive charge. Since they are both sitting on the
We know that
We know that
We can rewrite this as:
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What are the unit(s) of Coulomb's constant 
?
What are the unit(s) of Coulomb's constant
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To determine this, we have to solve for 
in Coulomb's law and then determine its constants.
Recall that the magnitude of the electrostatic force between point charges is given as:
, 
is the force given in 
, 
and 
are the charges given in 
and 
is distance given in 
Solving for 
,
Writing out the terms on the left in their units:
Therefore, 
is given in 
To determine this, we have to solve for
Recall that the magnitude of the electrostatic force between point charges is given as:
Solving for
Writing out the terms on the left in their units:
Therefore,
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Two protons are at a distance 
away from each other. There is a force 
acting on each proton due to the other. If the protons are moved so that they are now at a distance
apart, what is the new force acting on each proton due to the other 
?
Two protons are at a distance
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Coulomb's law shows that the force between two charged particles is inversely proportional to the square of the distance between the particles.
If the distance between the charges is reduced by 
, that means the 
is squared in the denominator and the 
will flip up to the top to give 
time the original force. More explicitly, if we plug in the given information the initial force will be:
Coulomb's law shows that the force between two charged particles is inversely proportional to the square of the distance between the particles.
If the distance between the charges is reduced by
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Determine the strength of a force of proton on another proton in the nucleus if they are 
apart.
Determine the strength of a force of proton on another proton in the nucleus if they are
Tap to reveal answer
Use Coulomb's law:
, where 
is Coulomb's constant, 
are charges of the two points and 
is the distance between the charges.
Use Coulomb's law:
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If the distance between two charged particles is doubled, the strength of the electric force between them will .
If the distance between two charged particles is doubled, the strength of the electric force between them will .
Tap to reveal answer
Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:
The strength of the force will be inversely proportional to the square of the distance between the charges.
When the distance between the charges is doubled, the total force will be divided by four (quartered).
Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:
The strength of the force will be inversely proportional to the square of the distance between the charges.
When the distance between the charges is doubled, the total force will be divided by four (quartered).
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An excess charge of is put on an ideal neutral conducting sphere with radius . What is the Coulomb force this excess charge exerts on a point charge of that is from the surface of the sphere?
An excess charge of
Tap to reveal answer
Two principal realizations help with solving this problem, both derived from Gauss’ law for electricity:
-
The excess charge on an ideal conducting sphere is uniformly distributed over its surface
-
A uniform shell of charge acts, in terms of electric force, as if all the charge were contained in a point charge at the sphere’s center
With these realizations, an application of Coulomb’s law answers the question. If is the point charge outside the sphere, then the force on is:
In this equation, is Coulomb’s constant, is the excess charge on the spherical conductor, and is total distance in meters of from the center of the conducting sphere.
Using the given values in this equation, we can calculate the generated force:
Two principal realizations help with solving this problem, both derived from Gauss’ law for electricity:
-
The excess charge on an ideal conducting sphere is uniformly distributed over its surface
-
A uniform shell of charge acts, in terms of electric force, as if all the charge were contained in a point charge at the sphere’s center
With these realizations, an application of Coulomb’s law answers the question. If
In this equation,
Using the given values in this equation, we can calculate the generated force:
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Charges A and B are placed a distance of from one another. The charge of particle A is whereas the charge of particle B is . Charge B experiences an electrostatic force of from charge A. Similarly, charge A experiences an electrostatic force of from charge B.
What is the ratio of to ?
Charges A and B are placed a distance of
What is the ratio of
Tap to reveal answer
This question is very simple if you realize that the force experienced by both charges is equal.
The definition of the two electrostatic forces are given by Coulomb's law:
In this question, we can rewrite this equation in terms of our given system.
It doesn’t matter if the charges of the two particles are different; both particles experience the same force because the charges of both particles are accounted for in the electrostatic force equation (Coulomb's law). This conclusion can also be made by considering Newton's third law: the force of the first particle on the second will be equal and opposite the force of the second particle on the first.
Since the forces are equal, their ratio will be .
This question is very simple if you realize that the force experienced by both charges is equal.
The definition of the two electrostatic forces are given by Coulomb's law:
In this question, we can rewrite this equation in terms of our given system.
It doesn’t matter if the charges of the two particles are different; both particles experience the same force because the charges of both particles are accounted for in the electrostatic force equation (Coulomb's law). This conclusion can also be made by considering Newton's third law: the force of the first particle on the second will be equal and opposite the force of the second particle on the first.
Since the forces are equal, their ratio will be
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Two protons are on either side of an electron as shown below:
The electron is 30 µm away from the proton on its left and 10 µm away from the proton on its right. What is the magnitude and direction of the net electric force acting on the electron?
A proton has a charge of
Two protons are on either side of an electron as shown below:
The electron is 30 µm away from the proton on its left and 10 µm away from the proton on its right. What is the magnitude and direction of the net electric force acting on the electron?
A proton has a charge of
Tap to reveal answer
The net force on the electron is the sum of the forces between the electron and each of the protons:
These forces are given by Coulomb's law:
Using the numbers given, we get:
Because opposite charges attract, points left (the negative direction) and points right (the positive direction).
Therefore, the net force is
Because this value is positive, the direction is rightward.
The net force on the electron is the sum of the forces between the electron and each of the protons:
These forces are given by Coulomb's law:
Using the numbers given, we get:
Because opposite charges attract,
Therefore, the net force is
Because this value is positive, the direction is rightward.
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If we have 2 charges, and , that are apart, what is the magnitude of the force exerted on by if we know that has a charge of and has a charge of ?
If we have 2 charges,
Tap to reveal answer
Use Coulomb's Law
Plug in known values and solve.
A negative value for electric force indicates an attractive force. This makes sense since our two charges have opposite signs. Since we're asked for magnitude, all answer choices are positive.
Use Coulomb's Law
Plug in known values and solve.
A negative value for electric force indicates an attractive force. This makes sense since our two charges have opposite signs. Since we're asked for magnitude, all answer choices are positive.
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If we have 2 charges, and , that are apart, what is the force exerted on by if we know that has a charge of and has a charge of ?
If we have 2 charges,
Tap to reveal answer
Use Coulomb's law.
Plug in known values and solve.
Note that the force between two charges of the same sign (both positive or both negative) is positive. This indicates the force is repulsive, which makes sense since both charges are positive.
Use Coulomb's law.
Plug in known values and solve.
Note that the force between two charges of the same sign (both positive or both negative) is positive. This indicates the force is repulsive, which makes sense since both charges are positive.
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