Electromagnetics - College Physics
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A parallel plate capacitor with no dielectric has capacitance 
. The distance between the capacitor plates is halved. What is the new capacitance?
A parallel plate capacitor with no dielectric has capacitance
The capacitance of a parallel plate capacitor is proportional to the inverse of the distance between the plates. If the distance is halved, the capacitance is doubled.
The capacitance of a parallel plate capacitor is proportional to the inverse of the distance between the plates. If the distance is halved, the capacitance is doubled.
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An RC circuit is connected to a 
power supply. If the resistance of the resistor is 
and the capacitance is 
, how long will it take for this capacitor to become fully charged?
An RC circuit is connected to a
The formula for finding the voltage of a simple RC circuit is
, where 
is the capacitor voltage, 
is the source voltage, 
is the resistance, and 
is the capacitance.
We want to know when the capacitor will reach the voltage of the power source 
so
and thus 
Using the properties of natural logs yields
Solving for 
yields 
The formula for finding the voltage of a simple RC circuit is
We want to know when the capacitor will reach the voltage of the power source
Using the properties of natural logs yields
Solving for
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Which of the following expressions gives the capacitance for a capacitor in a circuit in which the only factors known are a) the current through the circuit, b) the resistance of the circuit, and c) the charge that has accumulated on the capacitor?
Which of the following expressions gives the capacitance for a capacitor in a circuit in which the only factors known are a) the current through the circuit, b) the resistance of the circuit, and c) the charge that has accumulated on the capacitor?
In this question, we're given a number of parameters of a circuit and are asked to find how we can use these various parameters to show the capacitance of the circuit's capacitor.
First, recall what a capacitor is; something that stores charge for a given voltage difference. In other words, when there is a voltage difference between the two plates of a capacitor, a certain amount of charge can be stored on these plates. The more charge that can be stored for a given voltage difference, the greater that capacitor's capacitance. This can be shown by the following equation.
From the above expression, 
is the capacitance which we are trying to find a proper expression for. 
is the charge accumulated on the plates, which is one parameter we're given. Voltage, 
, on the other hand, is not provided.
To put the voltage into different terms, we'll need to use Ohm's law, which states the following.
In other words, the voltage is proportional to both the current and the resistance of the circuit.
Since we are given both current and resistance as known parameters in the question stem, we can use these for our final answer. By substituting the 
in the capacitance expression with 
, we obtain the following answer.
In this question, we're given a number of parameters of a circuit and are asked to find how we can use these various parameters to show the capacitance of the circuit's capacitor.
First, recall what a capacitor is; something that stores charge for a given voltage difference. In other words, when there is a voltage difference between the two plates of a capacitor, a certain amount of charge can be stored on these plates. The more charge that can be stored for a given voltage difference, the greater that capacitor's capacitance. This can be shown by the following equation.
From the above expression,
To put the voltage into different terms, we'll need to use Ohm's law, which states the following.
In other words, the voltage is proportional to both the current and the resistance of the circuit.
Since we are given both current and resistance as known parameters in the question stem, we can use these for our final answer. By substituting the
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What is the main difference between electrical and gravitational forces?
What is the main difference between electrical and gravitational forces?
Electric forces can be attractive or repulsive because charges may be positive or negative. In the case for gravitational forces, there are only attractive forces because mass is always positive.
Electric forces can be attractive or repulsive because charges may be positive or negative. In the case for gravitational forces, there are only attractive forces because mass is always positive.
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When the magnitude of two interacting charges is increased by a factor of 2, the electrical forces between these charges is __________.
When the magnitude of two interacting charges is increased by a factor of 2, the electrical forces between these charges is __________.
In Coloumb's law, an increase in both interacting charges will cause an increase in the magnitude of the electrical force between them. Specifically if the magnitude of both interacting charges is doubled, this will quadruple the electrical force.
In Coloumb's law, an increase in both interacting charges will cause an increase in the magnitude of the electrical force between them. Specifically if the magnitude of both interacting charges is doubled, this will quadruple the electrical force.
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Three equal charges are at three of the corners of a square of side d. A fourth charge of equal magnitude is at the center of the square as shown in Figure above. Which of the arrows shown represents the net force acting on the charge at the center of the square?
Three equal charges are at three of the corners of a square of side d. A fourth charge of equal magnitude is at the center of the square as shown in Figure above. Which of the arrows shown represents the net force acting on the charge at the center of the square?
Because of the principles of superposition, each electric force that acts from the charges at the corners on to the charge at the center can be broken into components. Since all the charges are positive, all the forces will be repulsive. The forces acting from the top left and bottom right corners will cancel, leaving only the repulsive force coming from the bottom left corner.
Because of the principles of superposition, each electric force that acts from the charges at the corners on to the charge at the center can be broken into components. Since all the charges are positive, all the forces will be repulsive. The forces acting from the top left and bottom right corners will cancel, leaving only the repulsive force coming from the bottom left corner.
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An electron traveling along the +x-axis enters an electric field that is directed vertically down, i.e., along the negative y-axis. What will be the direction of the electric force acting on the electron after entering the electric field?
An electron traveling along the +x-axis enters an electric field that is directed vertically down, i.e., along the negative y-axis. What will be the direction of the electric force acting on the electron after entering the electric field?
Positive charges in an electric field will experience an electric force that is in the same direction as the electric field. If the charge is negative, the force will be in the opposite direction of the electric field. Since we are talking about an electron moving in an electric field that points in the negative y-direction, the electron will feel a force that points in the positive y-direction, or upwards.
Positive charges in an electric field will experience an electric force that is in the same direction as the electric field. If the charge is negative, the force will be in the opposite direction of the electric field. Since we are talking about an electron moving in an electric field that points in the negative y-direction, the electron will feel a force that points in the positive y-direction, or upwards.
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A charged rod carrying a negative charge is brought near two spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres?
A charged rod carrying a negative charge is brought near two spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres?
When the negatively charged rod is brought near one of the two spheres, the presents of the negative charge will induce a flow of charge in the spheres such that regions farthest away from the charged rod will become most negative and regions near the rod will become most positive. This is called charge by induction.
When the negatively charged rod is brought near one of the two spheres, the presents of the negative charge will induce a flow of charge in the spheres such that regions farthest away from the charged rod will become most negative and regions near the rod will become most positive. This is called charge by induction.
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By what method will a positively charged rod produce a negative charge on a conducting sphere that is placed on an insulating surface?
By what method will a positively charged rod produce a negative charge on a conducting sphere that is placed on an insulating surface?
Charge by induction happens when a charged object is brought in the vicinity of a neutral object. The presents of the charged object will cause the free charges in the neutral object to shift such that the neutral object becomes polarized. When the charged object is positive, this will induce a negative charge on a neutral object.
Charge by induction happens when a charged object is brought in the vicinity of a neutral object. The presents of the charged object will cause the free charges in the neutral object to shift such that the neutral object becomes polarized. When the charged object is positive, this will induce a negative charge on a neutral object.
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A charged particle traveling along the +x axis enters an electric field directed vertically upward along the +y-axis. If the charged particle experiences a force downward because of this field, what is the sign of the charge on this particle?
A charged particle traveling along the +x axis enters an electric field directed vertically upward along the +y-axis. If the charged particle experiences a force downward because of this field, what is the sign of the charge on this particle?
Positive charges in an electric field will experience an electric force that is in the same direction as the electric field. If the charge is negative, the force will be in the opposite direction of the electric field. Since the charged particle experiences a force which is opposite to the electric field, the sign of the charge must be negative.
Positive charges in an electric field will experience an electric force that is in the same direction as the electric field. If the charge is negative, the force will be in the opposite direction of the electric field. Since the charged particle experiences a force which is opposite to the electric field, the sign of the charge must be negative.
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An x-ray machine emits electromagnetic photons carrying a frequency of 
. What is the approximate energy carried by each photon?
An x-ray machine emits electromagnetic photons carrying a frequency of
The energy of a photon of a given frequency is determined by the equation
, where 
is Plank's constant 
So plug in Plank's constant and the frequency of the x-ray photons to get an energy of very near 
The energy of a photon of a given frequency is determined by the equation
So plug in Plank's constant and the frequency of the x-ray photons to get an energy of very near
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A single string of wire has a resistance of 
. If the wire is connected to a 
power source, what is the strength of the magnetic field 
away from the wire?
A single string of wire has a resistance of
So this is all about the magnetic field strength around a current carrying wire.
The equation for this is:
But you must use Ohm's Law 
in order to find the current in the wire.
Since the wire has 
of resistance and the voltage through the wire is 
, that means the current in the wire is 
.
Being sure to change 
into 
, plug everything in and get the answer, which is
So this is all about the magnetic field strength around a current carrying wire.
The equation for this is:
But you must use Ohm's Law
Since the wire has
Being sure to change
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A conductor is placed in an electric field under electrostatic conditions. Which of the following statements is correct for this situation?
A conductor is placed in an electric field under electrostatic conditions. Which of the following statements is correct for this situation?
A conductor is defined as a object free to move charges. In particular, valence electrons, which are the outer most electron in each atom and the most free to move, travel inside the conductor until the net electric field inside the conductor is zero. These electrons will move until this condition has been met. Because of the presents of charged particles at the surface and the condition that they are no longer moving, any electric field at the surface must be perpendicular to that surface.
A conductor is defined as a object free to move charges. In particular, valence electrons, which are the outer most electron in each atom and the most free to move, travel inside the conductor until the net electric field inside the conductor is zero. These electrons will move until this condition has been met. Because of the presents of charged particles at the surface and the condition that they are no longer moving, any electric field at the surface must be perpendicular to that surface.
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The figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have an electric flux of 
through them?
The figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have an electric flux of
Gauss' laws states that the the electric flux through a Gaussian surface will be proportional to the net total charge inside the Gaussian surface. By inspection of the figure, we see that Gaussian surface B is the correct answer.
Gauss' laws states that the the electric flux through a Gaussian surface will be proportional to the net total charge inside the Gaussian surface. By inspection of the figure, we see that Gaussian surface B is the correct answer.
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The Figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them
The Figure shows four Gaussian surfaces surrounding a distribution of charges. Which Gaussian surfaces have no electric flux through them
According to Gaussian law, the electric flux will be zero when the net electric charge inside the Gaussian surface is zero. By inspection, we see this is Gaussian surface C.
According to Gaussian law, the electric flux will be zero when the net electric charge inside the Gaussian surface is zero. By inspection, we see this is Gaussian surface C.
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Gaussian surfaces A and B enclose the same positive charge +Q. The area of Gaussian surface A is three times larger than that of Gaussian surface B. The flux of electric field through Gaussian surface A is __________.
Gaussian surfaces A and B enclose the same positive charge +Q. The area of Gaussian surface A is three times larger than that of Gaussian surface B. The flux of electric field through Gaussian surface A is __________.
According to Gauss's law, the total electric flux is equal to the net total electric charge inside the a Gaussian surface. If the Gaussian surface is three times larger, the electric flux will be the same if both Gaussian surfaces contain the same amount of total electric charge.
According to Gauss's law, the total electric flux is equal to the net total electric charge inside the a Gaussian surface. If the Gaussian surface is three times larger, the electric flux will be the same if both Gaussian surfaces contain the same amount of total electric charge.
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Which of the arrows shown in the figure represents the correct direction of the electric field between the two metal plates?
Which of the arrows shown in the figure represents the correct direction of the electric field between the two metal plates?
The direction of electric field describes the trajectory of a positive test charge. Since a positive test charge would want to move away from the positive metal plate and towards the negative metal plate, the direction would be A.
The direction of electric field describes the trajectory of a positive test charge. Since a positive test charge would want to move away from the positive metal plate and towards the negative metal plate, the direction would be A.
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Suppose that a magnetic field is oriented such that it is pointing directly to the left, as in the picture shown below. If a positively charged particle were to begin traveling through this magnetic field to the right, in which direction would the particle's trajectory begin to curve?
Suppose that a magnetic field is oriented such that it is pointing directly to the left, as in the picture shown below. If a positively charged particle were to begin traveling through this magnetic field to the right, in which direction would the particle's trajectory begin to curve?
In order to answer this question, it's important to understand the factors that determine the magnetic force experienced by a charge. We can begin by writing out the equation for magnetic force.
As shown in the above equation, the magnetic force is directly proportional to the particle's charge, its velocity, and the strength of the magnetic field itself. But, for the purposes of the this question, the most important factor is the angle of the particle's velocity with respect to the magnetic field.
Notice that if theta is equal to zero, then the sine of theta will be equal to zero as well. This, in turn, will cause the magnetic force to also be zero. This is also true if we were to define theta as 
.
Since the particle is moving in a direction that is parallel to the magnetic field lines but in the opposite direction, we have a situation in which theta is equal to 
. This means that the magnetic force on the particle is zero. As a result, the particle will continue to move through the magnetic field without changing its direction.
In order to answer this question, it's important to understand the factors that determine the magnetic force experienced by a charge. We can begin by writing out the equation for magnetic force.
As shown in the above equation, the magnetic force is directly proportional to the particle's charge, its velocity, and the strength of the magnetic field itself. But, for the purposes of the this question, the most important factor is the angle of the particle's velocity with respect to the magnetic field.
Notice that if theta is equal to zero, then the sine of theta will be equal to zero as well. This, in turn, will cause the magnetic force to also be zero. This is also true if we were to define theta as
Since the particle is moving in a direction that is parallel to the magnetic field lines but in the opposite direction, we have a situation in which theta is equal to
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What size resistor should be connected across the terminals of a 
battery to produce a current of 
?
What size resistor should be connected across the terminals of a
Ohm's law is 
.
In this case, 
and 
.
Solving for the resistance, 
, we get:
Substitute known values and solve for the unknown resistance:
Ohm's law is
In this case,
Solving for the resistance,
Substitute known values and solve for the unknown resistance:
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A 
battery is connected to a small heater with constant resistance 
. How much current flows through the heater?
A
Ohm's law relates voltage to current and resistance, 
. To find the current, we simply divide the voltage by the resistance and get 
Ohm's law relates voltage to current and resistance,
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