Electric PotentialElectric Potentialand Energyand Energy

ObjectivesObjectives

Define work and relate it to energyDefine work and relate it to energy

Define electric potential difference, and Define electric potential difference, and relate it to the work done on an electric relate it to the work done on an electric charge in an electric fieldcharge in an electric field

Define capacitanceDefine capacitance

Write equations for work, electric potential, Write equations for work, electric potential, and capacitanceand capacitance

Use equations to solve problemsUse equations to solve problems

Work is EnergyWork is EnergyCharge is stored at a “potential” or “voltage”Charge is stored at a “potential” or “voltage”– A battery stores a certain amount of charge at a A battery stores a certain amount of charge at a

specific voltagespecific voltage– When the charge runs out, the battery is “dead”When the charge runs out, the battery is “dead”– Unit of work is a joule (J), just like energy

Work is equal to a force exerted over a Work is equal to a force exerted over a distancedistance

Work is done to move a charge in Work is done to move a charge in an electric fieldan electric field

W = F · d

More SpecificallyMore Specifically

Positive work is Positive work is storedstored energy energy

Negative work is Negative work is releasedreleased energy energy

Work is only done if there is a component Work is only done if there is a component of the electric field in the direction of the of the electric field in the direction of the motionmotion– If the motion is perpendicular to the electric If the motion is perpendicular to the electric

field lines, no work is donefield lines, no work is done– The electric field is constant in that directionThe electric field is constant in that direction

WorkWork

W F d

EF

q

F q E

W q E d

W

qE d V

b g

∆V = Voltage or “potential difference”

VoltsVolts

Unit is joules per coulomb, or volt (V)Unit is joules per coulomb, or volt (V)

Potential difference, or voltage (V)Potential difference, or voltage (V)

VW

q

ExampleExample

Moving a charge of 3.2 x 10Moving a charge of 3.2 x 10-19-19 coulombs coulombs between two points in an electric field between two points in an electric field requires 4.8 x 10requires 4.8 x 10-18-18 joules of energy. joules of energy.

What is the potential difference between What is the potential difference between these points?these points?

SolutionSolution

q x C

W x J

VW

q

x J

x C

V V

3 2 10

4 8 10

4 8 10

3 2 10

15

19

18

18

19

.

.

.

.

ExampleExample

Electric field between two parallel platesElectric field between two parallel plates

+ + + + + + + + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

V = 60 V d = 3.0 cm

What is the magnitude of the electric field between them?

Textbook, Pg. 491

ExampleExample

An elementary charge is moved through a An elementary charge is moved through a potential difference of 1 voltpotential difference of 1 volt

Calculate the amount of work done on the Calculate the amount of work done on the chargecharge

SolutionSolution

V V

q x C

W

qV W qV

W V x C x J

1

16 10

1 16 10 16 10

19

19 19

.

. .

or 1 electronvolt (eV)

Electrical EnergyElectrical Energy

At A an electron has 100 eV of electric At A an electron has 100 eV of electric potential energypotential energy

At B the electron has 100 eV of kinetic At B the electron has 100 eV of kinetic energyenergy

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

eA

B

100 V

CapacitanceCapacitance

Capacitance depends on the structure of Capacitance depends on the structure of the devicethe device

A capacitor with a given amount of charge, A capacitor with a given amount of charge, will have a specific potential differencewill have a specific potential difference

Cq

V

CapacitanceCapacitance

Unit of capacitance is the farad (F)Unit of capacitance is the farad (F)

One farad equals one coulomb per voltOne farad equals one coulomb per volt

WARNING

Capacitors can be lethal

CA

d

For a parallel plate capacitor

SummarySummary

Electric potential differenceElectric potential difference– Work done per unit charge to move a charged Work done per unit charge to move a charged

body in an electric fieldbody in an electric field– Unit is joule per coulomb, or “volt”Unit is joule per coulomb, or “volt”

CapacitanceCapacitance– Ratio of an object’s stored charge to its Ratio of an object’s stored charge to its

potential differencepotential difference– Measured in faradsMeasured in farads

EquationsEquations

EF

qF q E

W F d W q E d

W

qE d V

Cq

V

b g

E = Electric Field

F = Force

q = Charge

W = Work = Electric Potential Energy

V = Potential Difference = Electric Potential

C = Capacitance

Practice ProblemsPractice Problems

Pg. 493 #5 – 8Pg. 493 #5 – 8