-conservative
Is the electric force conservative or non-conservative?
-electric potential energy
What type of potential energy is associate with the electric force?
-yes: electric potential energy
As such, is there a potential energy associated with the electric force?
-position of one charge with respect to another charge or a collection of charges
This form of potential energy is relative to the…?
PE = kqQ/r
When one charge q is separated from another charge Q by a distance r, the charges will have an electric potential energy equal to…?
-positive
If the charges are like charges, then the potential energy will be?
-negative
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…?
-the charge has more PE after being moved
Does the charge have more PE or less PE after being moved?
-positive
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…?
-the charge has less PE after being moved
Does the charge have more PE or less PE after being moved?
-the ratio of the magnitude of a charge’s change in electric potential energy to the magnitude of the charge itself
What is electric potential (V)?
ΔV = ΔPE/q
What is the equation that describes this relationship?
-scalar
Is potential energy a scalar or a vector?
-scalar
As such, is electric potential a scalar or a vector?
-joules
What is potential energy measured in?
-coulombs
What is charge measured in?
-joules per coulomb
Hence, the SI units of electric potential are…?
-the volt
What is this combination of units referred to as?
-the energy change an electron experiences when it moves through a potential difference of 1 V
What does an electron volt describe?
-positive
If two like charges are separated by a non-zero distance, is the electric potential energy positive or negative?
-negative
If two unlike charges are separated by a non-zero distance, is the electric potential energy positive or negative?
E = |Δv/Δr|
What equation describes the relationship between the electric field and the electric potential?
-either N/C or V/m
What are the two units that electric field can be expressed in?
-the rate of change of the electric potential with position
What does this equation demonstrate the electric field depends on?
-one moves in the direction of the electric field
It als follows that the electric potential decreases as…?
-the electric field is zero
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 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
-since the rate of change of a constant potential is zero, so too is the electric field
Why?
-it falls
When a ball is dropped in a gravitational field, what happens to its gravitational PE?
-KE increases
What happens to its KE?
-its KE increases
When the electrical PE of a change decreases, what happens to its KE?
-speed increases
What happens to the speed of the particle?
-conservative and nonconservative
What are the two pain types of work/forces?
-yes
Can conservative work be recovered?
-no
Can nonconservative work be recovered?
-the sum of PE and KE in a system
E = KE + PE
E = KE + PE
What is mechanical energy (E)?
-the energy of motion
What is KE?
-KE increases
-PE decreases
-PE decreases
When forces do positive work, what happens to KE? What happens to PE? (if work is conservative)
-KE decreases
-PE increases
-PE increases
When forces do negative work, what happens to KE? What happens to PE? (if work is conservative)
-KE decreases
-PE increases
-PE increases
A ball is thrown in the air. As it rises, what happens to both KE and PE?
-KE increases
-PE decreases
-PE decreases
As the ball falls, what happens to both KE and PE?
-KE decreases
-PE increases
-PE increases
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 increases
-PE decreases
-PE decreases
As the negative charge moves back towards the positive charge, what happens to both KE and PE?
PE electric = k*q1*q2/r
What formula describes electric potential energy?
-positive
If both charges are positive, what sign will PE have?
-positive
If both charges are negative, what sign will PE have?
-negative
If one charge is negative and one charge is positive, what sign will PE have?
+ ∞
What is the maximum value for PE?
– ∞
What is the lowest possible value for PE?
-origin
What is PE = 0 used as?
-lower
All systems seek to ______ PE as much as they can
-no
Does this necessarily mean that there will be any motion?
-electric potential
What is the name of the quantity “V”?
-how many joules of electric potential energy are available per coulomb at a given location
What is V?
-joules
What are the units of energy?
-couloumb
What are the units of charge?
-joules/coulomb
Therefore, what are the units of electric potential?
-other charges nearby
Where does electric potential com from?
-yes
Is V present whether or not there is anything to feel it?
-1 j/c
By definition, what is 1 volt?
-voltage
What is the nickname of electric potential?
-a lower voltage
Does a positive charge seek a higher or lower voltage?
-a lower voltage will lower the PE of the charge and increase the KE of the charge
Why?
-a higher 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?
– ∞
What is any charge’s PE dream value?
-no
Is this available in every system?
-by going to the lowest voltage possible
How does a positive charge achieve – ∞ ?
-by going to the highest voltage possible
How does a negative charge achieve – ∞ ?
-decreasing
Positive charges accelerate in the direction of _______ electric potential
-increasing
Negative charges accelerate in the direction of ________ electric potential
-greater than the final speed of the proton
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?
-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
-as a result, their final kinetic energies are equal
-since the electron has less mass than the proton, however, its speed must be greater
Why?
V = kq/r
What is the equation that describes the electric potential for a point charge?
-a change in potential from a distance of infinity to a distance r
In this expression, what does V actually represent?
PE = k*q1*q2/r
In addition to PE = qV, what is another equation that describes PE?
-zero
What is the electric potential energy of two charges separated by an infinite distance?
-positive sign
Since r is a distance, what sign will it always have?
-yes
Does V depend on the sign of the charge in question?
-the potential for positive charge increases to POSITIVE infinity near the ORIGIN and decreases to ZERO far away
The potential for positive charge increases to ____________ infinity near the ____________ and decreases to ________ far away.
-potential hill
Thus forming a?
-the potential for negative charge approaches NEGATIVE infinity near the ORIGIN.
The potential for negative charge approaches ____________ infinity near the ___________.
-potential well
Thus forming a?
-potential hill
If a positive charge sits at the origin, the electric potential (V) forms a…?
-potential well
If a negative charge sits at the origin, the electric potential (V) forms a…?
+∞ (seeks the highest r value possible)
A positive charge placed in the electric potential created by a positive charge will seek an r value of…?
-∞ (results in the lowest V value possible)
This will result in a V of…?
-∞ (results in the lowest PE value possible)
Which will result in a PE of…?
-∞ (seeks the lowest r value possible)
A negative charge placed in the electric potential created by a positive charge will seek an r value of?
+∞ (seeks the highest V value possible)
This will result in a V of…?
-∞ (seeks the lowest PE value possible)
Which will result in a PE of…?
-to gain a lower PE
What is the ultimate goal of any movement one of these charges experiences?
Q
What always controls the sign of V?
Suppose you have a system with a negative charge at the origin. What is the highest V available?
-∞ (seeks the lowest r value possible!)
A positive charge placed in the electric potential created by a negative charge will seek an r value of…?
-∞ (results in the lowest V value possible)
This will result in a V of…?
-∞ (results in the lowest PE value possible)
Which will result in a PE of…?
+∞ (seeks the highest r value possible)
A negative charge placed in an electric potential created by a negative charge will seek an r value of?
+∞ (results the highest V value possible)
This will result in a V of…?
-∞ (results in the lowest PE value possible)
Which will result in a PE of…?
-POSITIVE charges make voltage hills, NEGATIVE charges make voltage valleys
Review: _________ charges make __________, ________ charges make __________.
-positive charges like to ROLL DOWN voltage hills INTO voltage valleys
Positive charges like to ____________ voltage hills, ___________ into voltage valleys.
-Negative charges like to CLIMB voltage valleys. They also like to CLIMB voltage hills.
Negative charges like to _________ voltage valleys. They also like to __________ voltage hills.
-the value of the electrical potential (V)
On an equipotential, what do the contours represent?
-the electric field points in the direction of DECREASING electric potential
The electric field points in the direction of __________ electric potential
-the electric field is always PERPENDICULAR to the equipotential surfaces
The electric field is always ___________ to the equipotential surfaces.
-zero work
How much work is done when a charge is moved perpendicular to an electric field?
-because W = Fd(cosθ) is zero when the angle θ is 90 degrees
Why?
-no
Is it possible for equipotential surfaces to intersect?
-because each point on the map has only a single value of electric potential (V)
Why not?
Electric field lines always cross the EQUIPOTENTIALS at RIGHT ANGLES
Electric field lines always cross the ____________ at ______ _______.
-the electric field is more INTENSE where the equipotential surfaces are closely spaced
The electric field is more ___________ where the equipotential surfaces are closely spaced.
-yes
When working with several electric fields, is vector addition required?
-no
When working with voltage, is vector addition required?
-because voltage is not a vector, scalar addition can be used
Why not?
-the ability to calculate time
If you decide to work with voltage instead of electric field, what do you lose?
-the forces method
What type of calculation is at the core of an electric field calculation?
-the energy method
What type of calculation is at the core of a voltage calculation?
E = ΔV/Δr
What equation describes the relationship between energy and voltage?
-no
If a system as a constant voltage, will an electric field exist?
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.
Why not?
-towards lower voltage
In what direction does the electric field always point?
-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!
-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!
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.
-a weak electrical field
What do two equipotential lines that are far apart indicate?
-gradually/slowly
How quickly will energy exchange occur in a system with a weak electrical field?
-a strong electrical field
What do two equipotential lines that are close together indicate?
-rapidly
How quickly will energy exchange occur in a system with a strong electrical field?
-increases
When like charges are moved toward each other, the electric PE of the system…?
-decreases
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…?
-increases
When unlike charges are moved away from each other, the electric PE of the system…?
-the same
An equipotential line is one for which the potential at every point is…?
-zero
The potential difference between any two points on an equipotential is…?
-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
-therefore, the electric field in each of these regions 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?
-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
-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
If the electric field is zero in some region of space is the electric potential zero there as well? Explain.
-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
-in this case, the potential energy of the charge would change, and the surface would not in fact be an equipotential
Explain why equipotentials are always perpendicular to the electric field.
-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
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 terminals are connected to one another, the charges flow from plate to plate until both plates have zero charge
What becomes of the charge when the two terminals of the capacitor are connected to one another?
-the capacitance of a capacitor depends on (b) the separation of the plates and (e) the area of the plates
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?
-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
-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
The plates of a parallel plate capacitor are uncharged. Is the capacitance of this capacitor zero? Explain.
-the electron experiences an increasing electric potential
-due to the fact that increasing electric potential results in lower PE for negative charges
-due to the fact that increasing electric potential results in lower PE for negative charges
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.
-in a direction opposite to the electric field
In terms of the electric field, in what direction do electrons always move?
-in the direction of decreasing electric potential
In what direction does the electric field always point?
-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
-this is due to the fact that decreasing the electric potential results in a higher PE for positive charges
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 electric field remains the same
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 potential difference increases linearly with separation
Does the potential difference between the plates increase, decrease, or stay the same?
-the capacitance decreases inversely with teh separation
Does the capacitance of the plates 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
Does the energy stored within the capacitor increase, decrease, or stay the same?
-the electric field decreases
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 potential difference decreases
What happens to the potential difference between teh plates
-capacitance increases
What happens to the capacitance?
-the energy stored decreases
What happens to the energy stored in the capacitor?
-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
-it is therefore only possible to find higher voltages by going against the electric field, not with it
When is it possible for a charge to move to higher voltage in the same direction as the electric field?
