Potential & Field

Chapter 30

1

Potential & Field Chapter 30. Reading QuizzesChapter 30. Reading Quizzes

2

What quantity is represented by

the symbol ?

A. Electronic potential

B. Excitation potential

C. EMF

D. Electric stopping power

E. Exosphericity

3

What quantity is represented by

the symbol ?

A. Electronic potential

B. Excitation potential

C. EMF

D. Electric stopping power

E. Exosphericity

4

What is the SI unit of capacitance?

A. CapacitonA. Capaciton

B. Faraday

C. Hertz

D. Henry

E. Exciton

5

What is the SI unit of capacitance?

A. CapacitonA. Capaciton

B. Faraday

C. Hertz

D. Henry

E. Exciton

6

The electric field

A. is always perpendicular to an

equipotential surface.

B. is always tangent to an B. is always tangent to an

equipotential surface.

C. always bisects an equipotential

surface.

D. makes an angle to an equipotential

surface that depends on the amount

of charge.7

The electric field

A. is always perpendicular to an

equipotential surface.

B. is always tangent to an B. is always tangent to an

equipotential surface.

C. always bisects an equipotential

surface.

D. makes an angle to an equipotential

surface that depends on the amount

of charge.8

This chapter investigated

A. parallel capacitors A. parallel capacitors

B. perpendicular capacitors

C. series capacitors.

D. Both a and b.

E. Both a and c.

9

This chapter investigated

A. parallel capacitors A. parallel capacitors

B. perpendicular capacitors

C. series capacitors.

D. Both a and b.

E. Both a and c.

10

Connecting Potential and Field

11

Finding Electric Field from

Potential and Vice Versa

12

Finding the Electric Field from

the PotentialIn terms of the potential, the component of the electric field

in the s-direction is

Now we have reversed Equation 30.3 and have a way to

find the electric field from the potential.

EXAMPLE 30.4 Finding E from

the slope of VQUESTION:

EXAMPLE 30.4 Finding E from

the slope of V

EXAMPLE 30.4 Finding E from

the slope of V

EXAMPLE 30.4 Finding E from

the slope of V

EXAMPLE 30.4 Finding E from

the slope of V

EXAMPLE 30.4 Finding E from

the slope of V

20

Batteries and emfThe potential difference between the terminals of an ideal

battery is

In other words, a battery constructed to have an emf of In other words, a battery constructed to have an emf of

1.5V creates a 1.5 V potential difference between its

positive and negative terminals.

The total potential difference of batteries in series is simply

the sum of their individual terminal voltages:

21

Kirchoff’s Laws

∑∑ =outin

II

1. Junction Law. Net current at a junction is zero

(Conservation of Charge)

22

1. Loop Law. The sum of all potential differences around a

closed path is zero (Conservation of Energy)

Potential and Current

where R = ρL/A

23

where R = ρL/A

Electrical Circuit

� A circuit diagram is a simplified

representation of an actual circuit

� Circuit symbols are used to

represent the various elements

� Lines are used to represent wires

� The battery’s positive terminal is

indicated by the longer line

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indicated by the longer line

Electrical Circuit

25

+−

+−

+−

+−

Conducting wires.

In equilibrium all the points of the

wires have the same potential

Electrical Circuit

+−

+− The battery is characterized by the voltage –

the potential difference between the contacts of

the battery

In equilibrium this potential difference is equal to

the potential difference between the plates of the

capacitor.

V∆

26

V∆ capacitor.

Then the charge of the capacitor is

Q C V= ∆

If we disconnect the capacitor from the battery the

capacitor will still have the charge Q and potential

difference V∆

+−

V∆

Electrical Circuit

+−

+−

V∆

Q C V= ∆

If we connect the wires the charge will disappear

+−

V∆

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V∆If we connect the wires the charge will disappear

and there will be no potential difference

0V∆ =

Capacitors in Parallel

+−

V∆

+−

V∆

1C

2C

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+−

V∆

All the points have

the same potentialAll the points have

the same potential

The capacitors 1 and 2 have the same potential difference V∆

Then the charge of capacitor 1 is 1 1Q C V= ∆

The charge of capacitor 2 is 2 2Q C V= ∆

Capacitors in Parallel

+−

V∆

+−V∆

1C

2CThe total charge is

1 1Q C V= ∆

2 2Q C V= ∆

1 2Q Q Q= +

1 2 1 2( )Q C V C V C C V= ∆ + ∆ = + ∆

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+−

V∆

eqQ C V= ∆

This relation is equivalent to

the following one

1 2eqC C C= +

+−

+−

eqC

Capacitors in Parallel

� The capacitors can be replaced with

one capacitor with a capacitance of

� The equivalent capacitor must have

exactly the same external effect on the

circuit as the original capacitors

eqC

30

eqQ C V= ∆

Capacitors

31

+−

+−

V∆

eqQ C V= ∆

The equivalence means that

Capacitors in Series

+−

1V∆

+−

2V∆

1C 2C

32

+−

V∆

1C

1 2V V V∆ = ∆ + ∆

Capacitors in Series

+−

1V∆

+−

2V∆

C

1 2

1 2

Q QV V V

C C∆ = ∆ + ∆ = +

The total charge

is equal to 01 2Q Q Q= =

1 1Q C V= ∆2 2Q C V= ∆

33

+−

V∆

1C 2C

eq

QV

C∆ =

1 2

1 1 1

eqC C C= +

1 2

1 2

eq

C CC

C C=

+

Capacitors in Series

� An equivalent capacitor can be found

that performs the same function as the

series combination

� The potential differences add up to the

battery voltage

34

Quiz: Find the equivalent capacitance for the circuit.

in parallel

1 2 1 3 4eqC C C= + = + =

6C C C= + =

35

in parallel

1 2 8eqC C C= + =

in series

1 2

1 2

8 84

8 8eq

C CC

C C

⋅= = =

+ +in parallel

1 2 6eqC C C= + =

Example

in parallel

1 2 1 3 4eqC C C= + = + =

6C C C= + =

36

in parallel

1 2 8eqC C C= + =

in series

1 2

1 2

8 84

8 8eq

C CC

C C

⋅= = =

+ +in parallel

1 2 6eqC C C= + =

Q C V= ∆

37

Quiz: what are the charges stored?

38

39

� Assume the capacitor is being charged

and, at some point, has a charge q on it

� The work needed to transfer a small

charge from one plate to the other is

equal to the change of potential energy

Energy Stored in a Capacitor

q A

q∆

q

40

� If the final charge of the capacitor is Q,

then the total work required is

q− B

qdW Vdq dq

C= ∆ =

2

0 2

Q q QW dq

C C= =∫

� The work done in charging the capacitor is

equal to the electric potential energy U of a

capacitor

Energy Stored in a Capacitor

Q

2

0 2

Q q QW dq

C C= =∫

Q C V= ∆

41

This applies to a capacitor of any geometry

Q−

221 1

( )2 2 2

QU Q V C V

C= = ∆ = ∆

One of the main application of capacitor:

� capacitors act as energy reservoirs that can be

slowly charged and then discharged quickly to

Energy Stored in a Capacitor: Application

221 1

( )2 2 2

QU Q V C V

C= = ∆ = ∆

42

provide large amounts of energy in a short pulse

Q

Q−

Q C V= ∆

43

The Energy in the Electric

Field

The energy density of an electric field, such as the one

inside a capacitor, is

The energy density has units J/m3.

44

45

Dielectrics• The dielectric constant, like density or specific heat, is a

property of a material.

• Easily polarized materials have larger dielectric constants

than materials not easily polarized.

• Vacuum has κ = 1 exactly.• Vacuum has κ = 1 exactly.

• Filling a capacitor with a dielectric increases the

capacitance by a factor equal to the dielectric constant.

46

Chapter 30. Summary SlidesChapter 30. Summary Slides

General Principles

General Principles General Principles

Important Concepts Important Concepts

Applications Applications

Chapter 30. QuestionsChapter 30. Questions

What total potential difference is

created by these three batteries?

A. 1.0 V

B. 2.0 V

C. 5.0 V

D. 6.0 V

E. 7.0 V

What total potential difference is

created by these three batteries?

A. 1.0 V

B. 2.0 V

C. 5.0 V

D. 6.0 V

E. 7.0 V

Which potential-energy

graph describes this

electric field?

Which potential-energy

graph describes this

electric field? Which set of equipotential surfaces

matches this electric field?

Which set of equipotential surfaces

matches this electric field?

Three charged, metal

spheres of different radii

are connected by a thin

metal wire. The potential

and electric field at the

surface of each sphere

are V and E. Which of

the following is true?

A. V1 = V2 = V3 and E1 > E2 > E3

B. V1 > V2 > V3 and E1 = E2 = E3

C. V1 = V2 = V3 and E1 = E2 = E3

D. V1 > V2 > V3 and E1 > E2 > E3

E. V3 > V2 > V1 and E1 = E2 = E3

the following is true?

Three charged, metal

spheres of different radii

are connected by a thin

metal wire. The potential

and electric field at the

surface of each sphere

are V and E. Which of

the following is true?

A. V1 = V2 = V3 and E1 > E2 > E3

B. V1 > V2 > V3 and E1 = E2 = E3

C. V1 = V2 = V3 and E1 = E2 = E3

D. V1 > V2 > V3 and E1 > E2 > E3

E. V3 > V2 > V1 and E1 = E2 = E3

the following is true?Rank in order, from largest to smallest, the

equivalent capacitance (C ) to (C ) of equivalent capacitance (Ceq)a to (Ceq)d of

circuits a to d.A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c

B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a

C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d

D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c

E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b

Rank in order, from largest to smallest, the

equivalent capacitance (C ) to (C ) of

A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c

B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a

C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d

D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c

E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b

equivalent capacitance (Ceq)a to (Ceq)d of

circuits a to d.