Electric Potential AP Physics: M. Blachly Textbook: 17:1-3.

Electric Electric PotentialPotential

AP Physics: M. BlachlyAP Physics: M. Blachly

Textbook: 17:1-3Textbook: 17:1-3

Review of Work

Work done by the force given by:

• W = F d cos()

• Positive: Force is in direction moved

• Negative: Force is opposite direction moved

• Zero: Force is perpendicular to direction moved

TnR

If a positive charge were moved from very far away on the right to one of the positions shown, at what position would it have the greatest amount of stored energy?

+ ABCD

Work on Charges

Work, force, electric field and Electrical Energy are always considered from the point of view of a positive charge.

Electrostatic Potential Energy and Potential Difference

The electrostatic force is conservative – potential energy can be defined

Change in electric potential energy is negative of work done by electric force:

(17-1)

Electrostatic PE and Potential Difference

Electric potential (Voltage) is defined as potential energy per unit charge:

(17-2a)

TnR

Given the definition of the voltage, what would be the proper units for Voltage?

A.Joules

B.Joules/Volt

C.Joules/Coulomb

D.Volts/Coulomb

Electrostatic PE and Potential Difference

Electric potential is defined as potential energy per unit charge:

(17-2a)

Unit of electric potential: the volt (V).

1 V = I J/C.

17.1 Electrostatic Potential Energy

Only changes in potential can be measured, allowing free assignment of V = 0. (like solving gravitational PE problems)

(17-2b)

17.1 Electrostatic PE

Analogy between gravitational and electrical potential energy:

Electric Potential and Electric Field

Work is charge multiplied by potential:

Work is also force multiplied by distance:

Equi-potential Lines

17.3 Equipotential Lines

An equipotential is a line or surface over which the potential is constant.

Electric field lines are perpendicular to equipotentials.

The surface of a conductor is an equipotential.

17.3 Equipotential Lines

The electron

How much potential energy does a single electron have if it is moved across a potential of 1.0 volts?

19

19

so

1.6 10 C 1 V

1.6 10 J

UV

q

U qV

The Electron Volt, a Unit of Energy

One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt.

Potential Due to Point Charges

The electric potential due to a point charge can be derived using calculus.

(17-5)

212

2

C8.85 10

N×mo

Concept Check

A charge of 3.0 nC is placed at the origin. What is the voltage at a point that is 30. cm away?

V = 90 V

What about at a point that is a mile away?

V = 0.017 V

What about a point that is infinitely far away?

V = 0 V

Potential Due to Point Charges

These plots show the potential due to (a) positive and (b) negative charge.

Potential Due to Point Charges

Using potentials instead of fields can make solving problems much easier – potential is a scalar quantity, whereas the field is a vector.

Example: Old fashioned TV

An electron is accelerated across a potential of 5000 V. What is the velocity of the electron after passing through this potential difference?

Example: Old fashioned TV

An electron (m = 9.11E-31 kg) is accelerated across 5000 V. Find the velocity in terms of c.

21

2

PE KE

qV mv

19

31

7

2

2 1.6 10 C 5000 J

9.11 10 kg

4.19 10 m/s 0.140

qVv

m

v

v c

17.7 Capacitance

A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge.

17.7 Capacitance

Parallel-plate capacitor connected to battery. (b) is a circuit diagram.

Capacitance

Charge vs. Voltage for a Capacitor

Q = 0.5 V

0

1

2

3

4

5

6

0 2 4 6 8 10

Voltage (V)

Sto

red

Cha

rge

(C)

17.7 Capacitance

When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage:

(17-7)

The quantity C is called the capacitance.

Unit of capacitance: the farad (F)

TnR

What is a Farad?

A.Coulomb/Joule

B.Coulomb/Volt

C.Joule/Coulomb

D.Volt/Coulomb

Answer: B

17.7 Capacitance

The capacitance does not depend on the voltage; it is a function of the geometry and materials of the capacitor.

For a parallel-plate capacitor:

212

2

C8.85 10

N×m

o

o

AC

d

17.8 Dielectrics

A dielectric is an insulator, and is characterized by a dielectric constant K.

Capacitance of a parallel-plate capacitor filled with dielectric:

(17-9)

17.8 Dielectrics

Dielectric strength is the maximum field a dielectric can experience without breaking down.

17.8 Dielectrics

The molecules in a dielectric tend to become oriented in a way that reduces the external field.

17.8 Dielectrics

This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential.

TnR

For a capacitor connected to a battery of fixed voltage, what will adding a dielectric material do?A.Decrease the charge

storedB. Increase the charge storedC.It will not affect the amount

of charge stored.

Answer: B

17.9 Storage of Electric Energy

A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor.

221 1 1

2 2 2

QU QV CV

C

17.9 Storage of Electric Energy

The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field:

(17-11)

The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful!

17.9 Storage of Electric Energy

Heart defibrillators use electric discharge to “jump-start” the heart, and can save lives.

Camera’s use a capacitor discharge to fire the flash

17.10 Cathode Ray Tube

A cathode ray tube contains a wire cathode that, when heated, emits electrons. A voltage source causes the electrons to travel to the anode.

17.10 Cathode Ray Tube

The electrons can be steered using electric fields.

17.10 Cathode Ray Tube

Televisions and computer monitors (except for LCD and plasma models) have a largecathode ray tube as their display. Variations in the field steer the electrons on their way to the screen.

17.11 The Electrocardiogram (ECG or EKG)

The electrocardiogram detects heart defects by measuring changes in potential on the surface of the heart.

Summary of Chapter 17

• Electric potential energy:

• Electric potential difference: work done to move charge from one point to another

• Relationship between potential difference and field:

Summary of Chapter 17

• Equipotential: line or surface along which potential is the same

• Electric potential of a point charge:

Summary of Chapter 17

• Capacitor: nontouching conductors carrying equal and opposite charge

•Capacitance:

• Capacitance of a parallel-plate capacitor:

Summary of Chapter 17

• A dielectric is an insulator

• Dielectric constant gives ratio of total field to external field

• Energy density in electric field:

Capacitor Networks

When there are multiple capacitors in series, the capacitors will all have the same charge.

1 2 1 2

1 2

1 2

1 2

[1] and [2]

Since , we can rewrite [2] as

and since Q is all the same,

1 1 1 capacitor network in series

n n

n

n

n

Q Q Q V V V

Q CV

Q Q Q

C C C

C C C

Example Problem: Series

What is the equivalent capacitance of a network consisting of a 9.0 µF capacitor and a 18 µF capacitor in series? (Answer in µF).

What will be the charge on the smaller capacitor if this network is connected to a 12 volt battery? (Answer in µC )

What will be the voltage on the bigger capacitor?

Capacitor Networks

When there are multiple capacitors in parallel, the capacitors will all have the same voltage.

1 2 1 2

1 1 2 2

1 2

[1] and [2]

Since , we can rewrite [2] as

and since V is all the same,

capacitor network in parallel

n n

n n

n

V V V Q Q Q

Q CV

V C VC V C

C C C

Example Problem: Parallel

What is the equivalent capacitance of a network consisting of a 9.0 µF capacitor and a 18 µF capacitor in parallel? (Answer in µF).

What will be the voltage on the smaller capacitor if this network is connected to a 12 volt battery? (Answer in V )

What will be the charge on the smaller capacitor? (Answer in µC )

Example: Capacitors

Example: Capacitors

Example: Capacitors