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Chapter 20: Electric Potential Energy and the Electric Potential

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Is the electric force conservative or non-conservative?
-conservative
What type of potential energy is associate with the electric force?
-electric potential energy
As such, is there a potential energy associated with the electric force?
-yes: electric potential energy
This form of potential energy is relative to the...?
-position of one charge with respect to another charge or a collection of charges
When one charge q is separated from another charge Q by a distance r, the charges will have an electric potential energy equal to...?
PE = kqQ/r
If the charges are like charges, then the potential energy will be?
-positive
If the charges are unlike charges, then the potential energy will be...?
-negative
Suppose a positive test charge is placed in an electric field. If it is moved upward through a distance, the work done by the electric force is...?
-negative
Does the charge have more PE or less PE after being moved?
-the charge has more PE after being moved
Suppose a negative test charge is placed in an electric field. If it is moved upward through a distance, the work done by the electric force is...?
-positive
Does the charge have more PE or less PE after being moved?
-the charge has less PE after being moved
What is electric potential (V)?
-the ratio of the magnitude of a charge's change in electric potential energy to the magnitude of the charge itself
What is the equation that describes this relationship?
ΔV = ΔPE/q
Is potential energy a scalar or a vector?
-scalar
As such, is electric potential a scalar or a vector?
-scalar
What is potential energy measured in?
-joules
What is charge measured in?
-coulombs
Hence, the SI units of electric potential are...?
-joules per coulomb
What is this combination of units referred to as?
-the volt
What does an electron volt describe?
-the energy change an electron experiences when it moves through a potential difference of 1 V
If two like charges are separated by a non-zero distance, is the electric potential energy positive or negative?
-positive
If two unlike charges are separated by a non-zero distance, is the electric potential energy positive or negative?
-negative
What equation describes the relationship between the electric field and the electric potential?
E = |Δv/Δr|
What are the two units that electric field can be expressed in?
-either N/C or V/m
What does this equation demonstrate the electric field depends on?
-the rate of change of the electric potential with position
It als follows that the electric potential decreases as...?
-one moves in the direction of the electric field
In a certain region of space, the electric potential V is known to be constant. Is the electric field in this region positive, negative, or zero?
-the electric field is zero
Why?
-the electric field is related to the rate of change of the electric potential
-since the rate of change of a constant potential is zero, so too is the electric field
When a ball is dropped in a gravitational field, what happens to its gravitational PE?
-it falls
What happens to its KE?
-KE increases
When the electrical PE of a change decreases, what happens to its KE?
-its KE increases
What happens to the speed of the particle?
-speed increases
What are the two pain types of work/forces?
-conservative and nonconservative
Can conservative work be recovered?
-yes
Can nonconservative work be recovered?
-no
What is mechanical energy (E)?
-the sum of PE and KE in a system
E = KE + PE
What is KE?
-the energy of motion
When forces do positive work, what happens to KE? What happens to PE? (if work is conservative)
-KE increases
-PE decreases
When forces do negative work, what happens to KE? What happens to PE? (if work is conservative)
-KE decreases
-PE increases
A ball is thrown in the air. As it rises, what happens to both KE and PE?
-KE decreases
-PE increases
As the ball falls, what happens to both KE and PE?
-KE increases
-PE decreases
A force is applied to a negative charge that moves it away from a positive charge. As the negative charge moves away, what happens to both KE and PE?
-KE decreases
-PE increases
As the negative charge moves back towards the positive charge, what happens to both KE and PE?
-KE increases
-PE decreases
What formula describes electric potential energy?
PE electric = kq1q2/r
If both charges are positive, what sign will PE have?
-positive
If both charges are negative, what sign will PE have?
-positive
If one charge is negative and one charge is positive, what sign will PE have?
-negative
What is the maximum value for PE?
+ ∞
What is the lowest possible value for PE?
- ∞
What is PE = 0 used as?
-origin
All systems seek to ______ PE as much as they can
-lower
Does this necessarily mean that there will be any motion?
-no
What is the name of the quantity "V"?
-electric potential
What is V?
-how many joules of electric potential energy are available per coulomb at a given location
What are the units of energy?
-joules
What are the units of charge?
-couloumb
Therefore, what are the units of electric potential?
-joules/coulomb
Where does electric potential com from?
-other charges nearby
Is V present whether or not there is anything to feel it?
-yes
By definition, what is 1 volt?
-1 j/c
What is the nickname of electric potential?
-voltage
Does a positive charge seek a higher or lower voltage?
-a lower voltage
Why?
-a lower voltage will lower the PE of the charge and increase the KE of the charge
Does a negative charge seek a higher or lower voltage?
-a higher voltage will lower the PE of the charge and increase the KE of the charge
What is any charge's PE dream value?
- ∞
Is this available in every system?
-no
How does a positive charge achieve - ∞ ?
-by going to the lowest voltage possible
How does a negative charge achieve - ∞ ?
-by going to the highest voltage possible
Positive charges accelerate in the direction of _______ electric potential
-decreasing
Negative charges accelerate in the direction of ________ electric potential
-increasing
An electron with a negative charge accelerates from rest through a potential difference V. A proton with the same charge accelerates from rest through a potential difference of -V. Is the final speed of the electron more than, less than, or the same as the final speed of the proton?
-greater than the final speed of the proton
Why?
-the electron and proton have charges of equal magnitude, and therefore they have equal charges in electric potential energy
-as a result, their final kinetic energies are equal
-since the electron has less mass than the proton, however, its speed must be greater
What is the equation that describes the electric potential for a point charge?
V = kq/r
In this expression, what does V actually represent?
-a change in potential from a distance of infinity to a distance r
In addition to PE = qV, what is another equation that describes PE?
PE = kq1q2/r
What is the electric potential energy of two charges separated by an infinite distance?
-zero
Since r is a distance, what sign will it always have?
-positive sign
Does V depend on the sign of the charge in question?
-yes
The potential for positive charge increases to ____________ infinity near the ____________ and decreases to ________ far away.
-the potential for positive charge increases to POSITIVE infinity near the ORIGIN and decreases to ZERO far away
Thus forming a?
-potential hill
The potential for negative charge approaches ____________ infinity near the ___________.
-the potential for negative charge approaches NEGATIVE infinity near the ORIGIN.
Thus forming a?
-potential well
If a positive charge sits at the origin, the electric potential (V) forms a...?
-potential hill
If a negative charge sits at the origin, the electric potential (V) forms a...?
-potential well
A positive charge placed in the electric potential created by a positive charge will seek an r value of...?
+∞ (seeks the highest r value possible)
This will result in a V of...?
-∞ (results in the lowest V value possible)
Which will result in a PE of...?
-∞ (results in the lowest PE value possible)
A negative charge placed in the electric potential created by a positive charge will seek an r value of?
-∞ (seeks the lowest r value possible)
This will result in a V of...?
+∞ (seeks the highest V value possible)
Which will result in a PE of...?
-∞ (seeks the lowest PE value possible)
What is the ultimate goal of any movement one of these charges experiences?
-to gain a lower PE
What always controls the sign of V?
Q
Suppose you have a system with a negative charge at the origin. What is the highest V available?
0
A positive charge placed in the electric potential created by a negative charge will seek an r value of...?
-∞ (seeks the lowest r value possible!)
This will result in a V of...?
-∞ (results in the lowest V value possible)
Which will result in a PE of...?
-∞ (results in the lowest PE value possible)
A negative charge placed in an electric potential created by a negative charge will seek an r value of?
+∞ (seeks the highest r value possible)
This will result in a V of...?
+∞ (results the highest V value possible)
Which will result in a PE of...?
-∞ (results in the lowest PE value possible)
Review: _________ charges make __________, ________ charges make __________.
-POSITIVE charges make voltage hills, NEGATIVE charges make voltage valleys
Positive charges like to ____________ voltage hills, ___________ into voltage valleys.
-positive charges like to ROLL DOWN voltage hills INTO voltage valleys
Negative charges like to _________ voltage valleys. They also like to __________ voltage hills.
-Negative charges like to CLIMB voltage valleys. They also like to CLIMB voltage hills.
On an equipotential, what do the contours represent?
-the value of the electrical potential (V)
The electric field points in the direction of __________ electric potential
-the electric field points in the direction of DECREASING electric potential
The electric field is always ___________ to the equipotential surfaces.
-the electric field is always PERPENDICULAR to the equipotential surfaces
How much work is done when a charge is moved perpendicular to an electric field?
-zero work
Why?
-because W = Fd(cosθ) is zero when the angle θ is 90 degrees
Is it possible for equipotential surfaces to intersect?
-no
Why not?
-because each point on the map has only a single value of electric potential (V)
Electric field lines always cross the ____________ at ______ _______.
Electric field lines always cross the EQUIPOTENTIALS at RIGHT ANGLES
The electric field is more ___________ where the equipotential surfaces are closely spaced.
-the electric field is more INTENSE where the equipotential surfaces are closely spaced
When working with several electric fields, is vector addition required?
-yes
When working with voltage, is vector addition required?
-no
Why not?
-because voltage is not a vector, scalar addition can be used
If you decide to work with voltage instead of electric field, what do you lose?
-the ability to calculate time
What type of calculation is at the core of an electric field calculation?
-the forces method
What type of calculation is at the core of a voltage calculation?
-the energy method
What equation describes the relationship between energy and voltage?
E = ΔV/Δr
If a system as a constant voltage, will an electric field exist?
-no
Why not?
Suppose you dropped a charge into this system. The charge would like to move towards a lower PE but there is no variation in voltage! The charge stays put, and thus we know that there is no electric field.
In what direction does the electric field always point?
-towards lower voltage
Describe why/how the electric field and voltage are related, using a scenario in which a charge is placed in a system where a gradual voltage drop occurs.
-suppose a charge is placed in a system where a gradual voltage drop occurs
-as a result the decrease in PE is gradual, while the increase in KE is gradual
-charge experiences a gradual speed increase
-if a charge speeds up gradually it has a small acceleration
-if a charge has a small acceleration, it experiences a small force
-if a charge experiences a small force, the electric field it sits in must be small/weak!
-->therefore, a gradual voltage drop implies a small electric field!
What do two equipotential lines that are far apart indicate?
-a weak electrical field
How quickly will energy exchange occur in a system with a weak electrical field?
-gradually/slowly
What do two equipotential lines that are close together indicate?
-a strong electrical field
How quickly will energy exchange occur in a system with a strong electrical field?
-rapidly
When like charges are moved toward each other, the electric PE of the system...?
-increases
When like charges are moved away from each other, the electric PE of the system...?
-decreases
When unlike charges are moved toward each other, the electric PE of the system...?
-decreases
When unlike charges are moved away from each other, the electric PE of the system...?
-increases
An equipotential line is one for which the potential at every point is...?
-the same
The potential difference between any two points on an equipotential is...?
-zero
In one region of space the electric potential has a positive constant value. In another region of space the potential has a negative constant value. What can be said about the electric field within each of these two regions of space?
-the electric field is a measure of how much the electric potential changes from one position to another
-therefore, the electric field in each of these regions is zero
If the electric field is zero in some region of space is the electric potential zero there as well? Explain.
-not necessarily
-the electric field is related to the rate of change in electric potential
-therefore, if the electric field is zero in some region of space, it follows that the electric potential is constant in that region
-the constant value of the electric potential may be zero, but it may also be positive or negative
Explain why equipotentials are always perpendicular to the electric field.
-if the electric field is not perpendicular to an equipotential, the field would do work on a charge that moves along the equipotential
-in this case, the potential energy of the charge would change, and the surface would not in fact be an equipotential
A capacitor is connected to a battery and full charged. What becomes of the charge on the capacitor when it is disconnected from the battery?
-when the capacitor is disconnected from the battery, the charge on the capacitor plages simply remains where it is--there is no way for it to go anywhere else
What becomes of the charge when the two terminals of the capacitor are connected to one another?
-when the terminals are connected to one another, the charges flow from plate to plate until both plates have zero charge
On which of the following quantities does the capacitance of the capacitor depend: (a) the charge on the plates; (b) the separation of the plates; (c) the voltage difference between the plates; (d) the electric field between the plates; or (e) the area of the plates?
-the capacitance of a capacitor depends on (b) the separation of the plates and (e) the area of the plates
The plates of a parallel plate capacitor are uncharged. Is the capacitance of this capacitor zero? Explain.
-no
-as an example, note that the volume of a milk container is not zero just because the container happens to be empty of milk
-the same can be said about the capacitance of a capacitor that happens to be uncharged
An electron is released from rest in a region of space with a nonzero electric field. As the electron moves, does it experience an increasing or decreasing electric potential? Explain.
-the electron experiences an increasing electric potential
-due to the fact that increasing electric potential results in lower PE for negative charges
In terms of the electric field, in what direction do electrons always move?
-in a direction opposite to the electric field
In what direction does the electric field always point?
-in the direction of decreasing electric potential
A proton is released from rest in a region of space with a nonzero electric field. As the proton moves, does it experience an increasing or decreasing electric potential? Explain.
-the proton experiences a decreasing electric potential
-this is due to the fact that decreasing the electric potential results in a higher PE for positive charges
The plates of a parallel-plate cap have constant charges of +Q and -Q. As the distance between the plates is increased, does the electric field increase, decrease, or remain the same?
-the electric field remains the same
Does the potential difference between the plates increase, decrease, or stay the same?
-the potential difference increases linearly with separation
Does the capacitance of the plates increase, decrease, or stay the same?
-the capacitance decreases inversely with teh separation
Does the energy stored within the capacitor increase, decrease, or stay the same?
-the energy stored win the capacitor increases linearly with separation due to the work required to move the plates farther apart
The plates of a parallel-plate capacitor have constant charges of +Q and -Q. When a dielectric is inserted, what happens to the electric field?
-the electric field decreases
What happens to the potential difference between teh plates
-the potential difference decreases
What happens to the capacitance?
-capacitance increases
What happens to the energy stored in the capacitor?
-the energy stored decreases
When is it possible for a charge to move to higher voltage in the same direction as the electric field?
-electric field lines always point towards lower voltage
-it is therefore only possible to find higher voltages by going against the electric field, not with it