1 lecture 1 electric charge structure of matter 08/30/2010 conductors and insulators charging...

1

Lecture 1

Electric ChargeStructure of Matter

08/30/2010

Conductors and InsulatorsCharging MechanismsCoulomb’s lawSuperposition principle

2Electric charge - experiments

Repulsion Attraction

Plexiglass

Plexiglass

Plexiglass

Plastic

4

Plexiglass Plastic

Plexiglass Repels Attracts

Plastic Attracts Repels

New physical property of matter: electric chargeelectric charge

Electric charge

Charged bodies interact through: electrical forceselectrical forces

Need two flavors to explain the existence of repulsive as well as

attractive forcespositive (+) and negative (-)positive (+) and negative (-)

5Microscopic view of matter

Elementary particles:

Number of electrons = Number of protons

The atom is neutral

6Electric charges

Like charges repel; opposite charges attract.

Examples of charges: electrons (negative); protons (positive)

Two types of charges: positive (+) and negative (-)

Type of materials: insulators, conductors (Ex metals), semiconductors

7Electric charge properties

Like charges repel; opposite charges attract.

Charge is discrete (quantized)- The smallest charge possible is = - Any charge is a integer multiple of the elementary unit of

charge

1.602 x 10-19 C (Coulombs)

Charge is conserved - charge can be exchanged between different parts of a closed system, but the total charge of the system cannot change

8Three pithballs are suspended from thin threads. It is found thatpithballs 1 and 2 repel each other and that pithballs 2 and 3 repel each other. From this we can conclude that:

1. 1 and 3 carry charges of opposite sign. 2. 1 and 3 carry charges of equal size.3. all three carry charges of the same sign.4. one of the objects carries no charge.5. we need to do more experiments

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

9

Types of materials

Conductors - charges move freely (Ex. metals). One consequence

of this property is that the charge that is transferred to a conductor will spread out uniformly on its surface. Insulators - charges do not move freely (Ex. glass, plastic). Semiconductors - intermediate case - charges can move freely under in some special cases (higher temperature, applied voltage) (silicon, germanium). Superconductors – extremely good conductors = zero

resistance. Restricted to very low temperatures. (Ex. niobium, BISCO)

10Electroscope and Van de Graaff generator

Electroscope: used to measured charge by measuring the deflection of charged metal foils

Van de Graaff generator.

11Charging mechanisms

Objects can become charged when elementary charged particles (most probably electrons) are transferred from one object to the other.

- When a glass rod and fur are rubbed together some electrons are transferred to the fur (triboelectricity)

12Charging by contact

- Electrons are transferred from the plastic rod to the metal ball

13When a neutral metal sphere is charged by contact with a positively charged glass rod, the sphere:

1. loses electrons 2. gains electrons3. loses protons4. gains protons

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

14

Charging by induction

- The copper rod is attracted to the charged glass rod even if initially is uncharged and does not contact the glass rod at any time.

15The diagram below shows a neutral metal sphere on a isolating pedestal. Which of the other diagrams shown, describes best the charge distribution on the sphere when a negatively charged rod is brought in its vicinity?

1. A 2. B3. C4. D

A B

C D

++++

----

++++

+++

++-++--

-++

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

16The diagram below shows three identical neutral metal spheres on a isolating pedestals, which are in contact. Which of the other diagrams shown, describes best the charge distribution on the spheres when a negatively charged rod is brought in its vicinity?

1. A 2. B3. C4. D

A B

C D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

17

A negatively charged plastic rod is brought in the vicinity of a neutral metal ball placed on a isolating pedestal. If the opposite side of the sphere is briefly connected to the ground and then the plastic rod is removed, what will the final charge on the ball be?1. The metal ball will be

neutral as initially. 2. The metal ball will be

positively charged3. The metal ball will be

negatively charged.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

18Solution

- Due to the interaction with the plastic rod, positive and negative charges will be separated on the ball. Through the grounding loop the electrons are transferred to the Earth which acts as an infinite sink or source of electrons, leaving the sphere with a deficit of electrons (positively charged)

19Three metal balls are suspended from thin threads. It is found that balls 1 and 2 attract each other and that balls 2 and 3 repel each other. From this we can definitely conclude that:

1. 1 and 3 carry charges of opposite sign. 2. 1 and 3 carry charges of the same sign.3. all three carry charges of the same sign.4. one of the objects carries no charge.5. we need to do more experiments

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

20

Coulomb's Law

Explored by Charles Augustin de Coulomb

rrqqkF 2

21

constanty permitivit - mN

C1085.8

CmN1099.8

41k

0

2

212

0

2

29

0

21

Coulomb's law properties

Inverse square law

2112 FF

Direction: along the line joining the charges

Attractive for unlike charges and repulsive for like charges

rrqqkF 2

21

Newton’s 3rd Law action reaction pair:

22Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces?

20

1. 1 2. 23. 34. 45. 56. 6

1 2 3 4 5 6

0% 0% 0%0%0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

23Which graph best represents the magnitude of the interaction force between two positively charged ions as a function of the distance separating them?

20

A B

C D

1 2 3 4

0% 0%0%0%

1. A 2. B3. C4. D

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

24

Coulomb's law vs. Newton law of gravitation

2

210-

221

2

29

221

kgmN106.6742 G ,

rmmGF :ngravitatio of law sNewton'

CmN108.99 k ,

rqq

kF :law sCoulomb'

Inverse square laws - force acting along the line joining the particles.

There are two kinds of charges, but only one type of mass.

Gravity is always attractive.

The electrostatic force, (e.g., between an electron and proton), is enormously stronger (~ 1035 times stronger)

25A hydrogen atom is composed of a nucleus containing a single proton, about which a single electron orbits. The electric force between the two particles is 2.3 x 1039 greater than the gravitational force! If we can adjust the distance between the two particles, can we find a separation at which the electric and gravitational forces are equal?

20

1. Yes, we must move the particles further apart. 2. Yes, we must move the particles closer, together.3. No, at any distance.

1 2 3

0% 0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

26

Superposition principle

When two or more charges each exert a force on a charge, the total force on that charge is the vector sum of the forces exerted by the individual charges.

Example: - Linear distribution

n21 F...FFF

What is the net force acting on q3?

27Solution:

cmrwhererqq

kF

cmrwhererqq

kF

on

on

0.4,

0.2,

23223

3232

13213

3131

Step 1 : - Calculate the force produce by each charge

opposite. are they since forces individual thebetween difference by thegiven is force total theof magnitude the-

213

312

23

3231323 r

qqk

rqq

kFFF ononontotal

Step 2 : - Add all the forces using vector summation rules

28

Example 2: - Planar distribution (vector nature of Coulomb's law)Find the magnitude and direction of the force on Q.

29

0 N 0.17N 0.17

N 0.46 N 0.23N 0.23

21

21

yonQyonQytotal

xonQxonQxtotal

FFF

FFF

the total force on charge Q acts only along x

Step 1 : - find the force exerted by each charge on Q

N 0.29

(0.5m)C)10C)(4.010(2

CNm109.0

rQq

kF 2

66

2

29

21

1onQQ)1(q

The components on the x and y axis of are:1onQF

1onQ x 1onQ

1onQ y 1onQ

F F cos 360 - α

F F sin 360 - α

with

-1

0.3sin α =0.60.5

α=sin (0.6) 36.86o

o1onQ x 1onQ

o1onQ y 1onQ

F F cos 323.13 0.232 N

F F sin 323.13 0.17 N

N 17.0αsinFF

N 232.0αcosFF

2onQy2onQ

2onQx2onQ

Step 2 : - Add the two forces (addition using components)

Obtain the F2onQ components in a similar way

30

+q +4q

L

Extra credit (5 points) – due Wednesday, September 7

Problem

Two free point charges +q and +4q are located a distanceL, apart. A third charge is placed so that the whole system is in equilibrium. Find the location, magnitude, and sign of the third charge.

31Review – dealing with vector summation

y

x

1F

2F

F1x F2x

F2y

F1y

1 2

theangles are always measured clockwise towards the positive x axis

x

1F

2F

Fx

Fy

y

F

111

111

sincos

FFFF

y

x

222

222

sincos

FFFF

y

x

For the sum vector

221121

221121

sinsincoscos

FFFFFFFFFF

yyy

xxx

angle tantan

magnitude

1

22

x

y

x

y

yx

FF

FF

FFF

Question: How do we express the sum vector parameters (F, ), if we know them for the individual vectors, i.e. (F1, 1) and (F2,

32Extracredit Problem – Assigned on 09/03/2010Two free point charges +q and +4q are located a distance L, apart. A third charge is placed so that the whole system is in equilibrium. Find the location, magnitude, and sign of the third charge.Solution:

Step 1: - determine the condition for the charge qo to be at equilibrium.

Call the new charge, q0, and let it be distance x from +q. The free-body diagram shows relationship of the two forces on the new charge:

xLxxLxxL

xLx

xLqq

kxqq

k

324)(

)(41

)(4

22

22

20

20

33

Step 2: - determine the condition for the charge q or 4q to be at equilibrium.

qqqqqLq

Lq

xLwhereLqq

kxqq

k

94

9449

)(4

9

3)(4

00220

220

qq94

0

34Problem (Chapter 21, Problem 4 – Page 574)

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Figure a). The electrostatic force acting on sphere 2 due to sphere 1 is F. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Figure b), then to sphere 2 (Figure c), and finally removed (Figure d). The electrostatic force that now acts on sphere 2 has magnitude F’. What is the ratio F’/F?

1 2 3 F12

q q 0 Fq/2 q q/2 F/2q/2 3q/4 3q/4 3F/8

35In the following diagram what is the direction of the electrostatic force on the negative charge -q?

1. 2. 3. 4. 5. none of the above

Q

Q

- q

201 2 3 4 5

0% 0% 0%0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

36In the figure a charged particle of charge (- q) is surrounded by two circular rings of charged particles. What is the net force on the central particle due to the other particles?

1.

2.

3.

4.

5.

j

j

j

j

j

2o

2

2o

2

2o

2

2o

2

2o

2

2o

2

r4q

R4q2

R4q2

R4q2

r4q2

r4q2

201 2 3 4 5

0% 0% 0%0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

37Two small charged objects attract each other with a force F when separated by a distance d. If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2 the force becomes:

1. F/16 2. F/83. F/4 4. F/25. F

201 2 3 4 5

0% 0% 0%0%0%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

38

Electric Field

Why do we need this concept?

- Coulomb's law describes action at distance (like gravitation).- Any charge changes the properties of the space around it.- We need a field to describe this change.

The notion of field is not a new one: - A field is a quantity that

is assigned a value at each point in a region of space

40

Back to the electric field

0qFE

- Units: N/C - E does not depend on the test charge q0.

00q

00q

F

F

Note: The rest of this chapter and chapter 23 are mostly dedicated tohow to determine the magnitude and orientation of different electric.

To calculate the electric field of a charge distribution use superposition

...EEEE 321total

41

Force on a charge in an electric field

EqF

The direction of the force acting on a point charge in an electric field depends on both the direction of the electric field and the sign of the charge.

Positive charge q0 placed in an electric field

Negative charge q0 placed in an electric field

-

42

rrq

41E 2

0

Electric field due to a point charge

rrq qkF 2

0

0qFE

1 lecture 1 electric charge structure of matter 08/30/2010 conductors and insulators charging...

Documents