Work done by a conservative force on an object depends only on...?
The INITIAL and FINAL positions of object NOT the path taken.
Potential energy is equal to ___ of work done by conservative force.
Negative.
Coulomb force is also ____ like gravitational force.
Conservative.
Work done by a conservative force can be reinterpreted as the ____ of the ____ in ____ assosiated with that force.
Work done by a conservative force can be reinterpreted as the NEGATIVE of the CHANGE in POTENTIAL ENERGY assosiated with that force.
The change in the electric potential energy of a system consisting of charge q moving through a displacement x in a constant electric field E is given by ....?
The negative charge of q times the x-component of the electric field times the displacement of charge along x-axis. [PE=-qEx x].
For positive charges, electric potential energy works much like ...?
Gravitational potential energy.
When a positive test charge is placed in an electric field it moves in the direction of...?
The field.
When a positive test charge is placed in an electric field it moves from ___ to ___?
A point of HIGHER potential energy to a point of LOWER potential energy.
When a positive test charge is placed in an electric field its electric potential energy...?
Decreases.
When a positive test charge is placed in an electric field its kinetic energy...?
Increases.
When a negative test charge is placed in an electric field it moves in the direction of...?
It moves OPPOSITE direction of the field.
When a negative test charge is placed in an electric field it moves from ____ to ____?
A point of LOWER potential energy to a point of HIGHER potential energy.
When a negative test charge is placed in an electric field its electric potential energy...?
Decreases.
When a negative test charge is placed in an electric field its kinetic energy...?
Increases.
If an electron is released from rest in a uniform electric field, the electric potential energy of the charge-field system...?
Decreases.
The electric potential difference V between points A and B is equal to ...?
The change in electric potential energy as a charge q moves from A --> B divided by the charge q [V=PE/q].
What is the measure of the change in electric potential energy per unit charge?
Electric potential difference.
What is the work per unit charge that would have to be done by some force to move a charge from point A --> B in the electric field?
Electric potential difference [V=-E x].
If a positive charge is given an initial velocity in the direction of high potential, what will happen?
It can move in that direction but will slow and finally turn around [like a ball tossed upward].
How can negative charges go in the direction of lower potential energy?
Work must be done.
If a negatively charged particle is placed at rest in an electric potential field that increases in the positive direction what will happen to the particle?
It will accelerate in the positive x-direction.
Does a more massive particle gain less kinetic energy than a lighter particle in traversing a given potential difference?
The LESS massive particle will have the GREATER energy change.
Where is the zero point of electric potential taken?
At infinity.
The electric potential created by a point charge q at any distance r from the charge is equal to?
k x the charge/distance [V=k q/r].
Electric potential [work per unit charge] required to move a test charge in from infinity to a distance from a positive point charge [q] _____ as the positive charge moves ____.
Increases; closer to q.
If two charges are of the same sign, PE is ___?
Positive.
If two charges are of opposite signs, PE is ___?
Negative.
How is work done on a charge by electric force is related to the change in electric potential energy of the charge?
W=-PE
How is change in electric potential energy between two points A and B related to potential difference between those points?
PE=q(Vb-Va)
Potential energy between points is equal to their charge times the potential difference between them.
How is work done on a charge by electric forces related to potential difference between two points?
W=-q(Vb-Va)
______ is required to move a charge between two points that are at the same electric potential.
No net work.
W=0 whenever ___?
Vb=Va.
When a conductor is in electrostatic equilibrium a net charge placed on it resides ___?
Entirely on its surface.
The electric field just outside the surface of a charged conductor in electrostatic equilibrium is ____?
Perpendicular to the surface.
The field inside a conductor in electrostatic equilibrium is ___?
Zero [E=0].
All points on the surface of a charged conductor in electrostatic equilibrium are ____?
At the same potential.
On the surface of a charged conductor in equilibrium the electric potential energy is ____?
Constant everywhere.
____ is required to move a charge between two points inside a conductor.
No work.
If work done is zero, the difference in electric potential between any two points inside a conductor is...?
Zero!
The electric potential is ___ inside a conductor and _______ at the surface.
The electric potential is CONSTANT EVERYWHERE inside a conductor and EQUAL TO THAT SAME VALUE at the surface.
Because the electric potential is constant inside a conductor and equal to that value at the surface, what is not required to move a charge from interior --> surface.
Work!
What is the electron volt [eV]?
Unit of energy; the kinetic energy that an electron gains when accelerated through a potential difference of 1 V.
1 eV =
1.60 x 10^-19 J.
An electron initially at rest accelerates through a potential difference of 1V, gaining kinetic energy KEe where are proton at rest accelerates through a potential difference of -1V gaining kinetic energy KEp. What is the relationship between KEe and KEp?
KEe=KEp.
What is an equipotential surface?
A surface on which all points are at the same potential.
Why is no work required to move a charge at a constant speed on an equipotential surface?
Potential difference between any two points is zero.
When a free electron is in an electric field it experiences a force acting ...? [with respect to the field]
Anti-parallel [opposite in direction].
If a proton and an electron are held apart a distance of 1m and then released what happens to force between them as they approach each other?
It gets larger.
If a proton and an electron are held apart a distance of 1m and then released which particle has larger acceleration at any one moment?
Electron.
What is the relationship between equipotential surfaces and the electric field?
Electric field at every point of an equipotential surface is perpendicular to the surface.
What would happen if the electric field had a component parallel to the equipotential surface?
That component would produce an electric force on a charge placed on the surface -- this force would do work on the charge in contradiction to the definition of an equipotential surface.
What is a capacitor?
An electric device for storing charge.
What do capacitors do?
Store energy to be given to a circuit.
What are some examples of how capacitors are used?
- To tune frequency of radio receivers.
- Eliminate sparking in automobile ignition systems.
- Store short-term energy for rapid release in electronic flash units.
What do capacitors consist of?
Two parallel metal plates of area A and equal but opposite charges -Q and +Q separated by a distance d.
When used in an electric circuit, what are capacitor plates connected to?
The positive and negative terminals of a battery or voltage source.
When capacitors are connected to a voltage source, what happens to electrons?
They are pulled off one of the plates leaving it with a charge of +Q and transferred through battery to other plate, leaving it with charge -Q.
When does the transfer of charge stop in a parallel-plate capacitor?
When the potential difference across the plates equals potential difference of battery.
What is the capacitance of a pair of conductors [capacitor]?
The ratio of the magnitude of the charge on either plate to the magnitude of the potential difference between plates [C=Q/V].
A ____ capacitance is needed to store a large amount of charge for a given applied voltage?
Large capacitance.
The capacitance of a device depends on ...?
The geometric arrangement of the conductors.
What is the charge on one plate?
Magnitude of the charge x area of plate [Q=oA].
What is the capacitance of a parallel-plate capacitor?
Permittivity of free space x area of one plate divided by distance between plates [C=eo A/d].
What kind of plates can store more charge?
Plates with larger area or plates with smaller plate separation.
Why does a small plate separation store more charge?
The positive charges on one plate will exert a stronger force on the negative charges on other plate.
The electric field between plates of a parallel-plate capacitor is ___ near the center but ___ near the edges.
UNIFORM near center NONUNIFORM near edges.
What are the two most simple configurations of two or more capacitors combined in circuits?
Parallel and series.
Capacitors in parallel both have the same...?
Potential difference V across them.
What is the total charge stored by two capacitors?
Q=Q1+Q2.
The voltage across a device [like a capacitor] has the same meaning as ...?
The potential difference across the device.
How is the equivalent capacitance of a parallel combination of capacitors related to individual capacitances?
Equivalent capacitance of a parallel capacitor is LARGER than any of the individual capacitances.
For a series combination of capacitors, the magnitude of charge on the plates must be?
The same!
What happens to all right plates and all left plates of capacitors in a series?
All right plates gain charges of -Q and all left plates have charges of +Q.
The potential difference across any number of capacitors in a series equals...?
The sum of the potential differences across the individual capacitors.
How is the equivalent capacitance of a series combination of capacitors related to individual capacitances?
Equivalent capacitance of a series combination is always SMALLER than any individual capacitance.
In a parallel combination what is equal and what is added?
Potential difference is equal and charge is added.
In a series combination what is equal and what is added?
Charge is equal and potential difference is added.
A capacitor is designed where one plate is large and other is small. If plates are connected to battery, what are charges on plates?
They have equal but opposite charges.
The energy stored by capacitors is the same as ...?
The work required to move charge onto the plates.
If a capacitor is initially uncharged so that plates are at same potential how much work is required to transfer a small amount of charge from one plate to the other?
Very little.
Once charge has been transferred onto plates, what happens?
A small potential difference appears between plates so work must be done to transfer additional charge against this potential difference.
What is the equation for the work required to move more charge through a potential difference between plates?
Potential difference times charge [W=VQ]
A plot of voltage vs. charge for a capacitor is ____ with a slope ____.
A straight line; slope = 1/C.
On a voltage vs. charge graph for a capacitor, teh total work required to charge the capacitor to a final charge Q is ___?
The area under the straight line, which equals QV/2.
What is the equation for the total work to charge a capacitor to final charge Q?
W= 1/2 Q V
What are three ways to express the energy stored in a capacitor?
Energy stored =
1/2QV
1/2C(V)^2
Q^2/2C
What happens when a capacitor has exceeded the energy that can be stored in it?
Coulomb forces between charges on plates become so strong that electrons jump across gap, discharging capacitor.
How should three capacitors and two batteries be connected so that capacitors will store maximum energy?
Three capacitors in parallel - capacitances add.
Batteries in series - potential differences add.
A parallel-plate capacitor is disconnected from a battery and the plates aer pulled a small distance farther apart. What happens to:
C
Q
E between plates
V
Energy stored in capacitor
Capacitance decreases.
Charge stays the same.
Electric field between plates stays the same.
Electric potential difference increases.
Energy stored in capacitor increases.
What is a dielectric?
An insulating material such as rubber, plastic or waxed paper.
What happens when a dielectric is inserted between plates of a capacitor?
Capacitance increases.
What is capacitance?
Ability of a body to store electric charge.
In a parallel-plate capacitor capacitance is ___ to surface area and ___ to distance between plates.
In a parallel-plate capacitor capacitance is DIRECTLY PROPORTIAL to surface area and INVERSELY PROPORTIONAL to distance between plates.
Why does capacitance increase when a dielectric is inserted between plates?
More charge can be stored because of the induced charge on the surface of the electrical insulator.
If the dielectric completely fills the space between plates, what happens to capacitance?
It is multiplied by factor k [dielectric constant].
What happens to voltage across plates when a dielectric is inserted between plates?
It is reduced by factor k.
For any given plate separation there is a maximum electric field that can be produced in the dielectric before what happens?
It breaks down and begins to conduct.
What is the maximum electric field produced in dielectric called?
Dielectric strength.
What is the dielectric strength for air?
3 x 10^6 V/m.
An electrolytic capacitor is often used to store ____ at ____.
An electrolytic capacitor is often used to store LARGE AMOUNTS OF CHARGE at LOW VOLTAGES.
What does an electrolytic capacitor consist of?
Metal foil in contact with an electrolyte.
What happens when a voltage is applied between foil and electrolyte in an electrolytic capacitor?
Thin layer of metal oxide [insulator] is formed on foil which serves as the dielectric.
What happens in an electrolytic capacitor if the polarity of the applied voltage is opposite that intended?
Oxide layer will be removed and capacitor will conduct rather than store charge.
A fully charged parallel-plate capacitor remains connected to a battery while a dielectric is slid between plates. What happens to:
C
Q
E between plates
V
Energy stored in capacitor
Capacitance increases.
Charge increases.
Electric field between plates stays the same.
Electric potential difference stays the same.
Energy stored in capacitor increases.
When is a molecule polarized?
When there is a separation between average positions of its negative and positive charges.
What kind of dielectric constants will materials composed of permanently polarized molecules have?
Large ks.
How can polarization be induced on symmetric molecules with no permanent polarization?
By an external electric field that causes charges to shift.
In a parallel-plate capacitor with a dielectric material between plates if temperature of dielectric increases what happens to capacitance?
Capacitance decreases.
If three unequal capacitors [uncharged] are connected in a series across a battery, which capacitor will have the largest voltage?
The capacitor with SMALLEST capacitance [voltage is inversely proportional to capacitance].
What happens to the stored energy in a parallel-plate capacitor if the plate separation is doubled while capacitor remains connected to battery?
- Potential difference remains the same.
- Capacitance is halved.
- Energy stored is decreased by a factor of 2.
A parallel-plate capacitor filled with air carries charge Q. The battery is disconnected and dielectric with k=2 is inserted between plates. What happens?
- Charge stays the same.
- Capacitance increases by 2x.
- Potential energy stored [voltage] decreases by 2x.
A parallel-plate capacitor is charged by a battery then disconnected and plate separation is increased. What happens?
- Electric field remains the same.
- Charge remains the same.
- Capacitance decreases.
- Electric potential difference increases.
- Energy stored in capacitor increases.
The largest potential difference appears across a capacitor in a series that...?
Has the largest capacitance.
After a proton is released from rest in a uniform electric field:
- Where will it be accelerated towards?
- What will its acceleration be?
- Move in direction of field [toward negative charges].
- Constant acceleration because it experiences constant electric force.