Chapter 23 Electric Charge and Matters

第二十三章 電荷與物質

Lightning What causes lightning?

Charge distribution in clouds

The first electrical machine

Electrostatic generators

The Van de Graaff generator

Static charge

Electric Charge

Origin of “electric”

In 1600, William Gilbert, physician to Queen Elizabeth I, was the first one to coin the word “electric”, deriving from elektron, which is Greek for amber.

As early as 600 B.C., Thales of Miletus noted that when the mineral amber rubbed by wool or fur, it could attract small pieces of straw or feathers.

In the first century B.C., the poet Lucretius noted that lodestone could attract iron and did not need to be rubbed.

ChargeCharge is a property of matter that causes it to produce and experience electrical and magnetic effects.

The subject of the electrical effects of charges at rest is called electrostatics.

The fact that like charge repel and unlike charge attract led Charles du Fay to surmise in 1733 that there are two kinds of charges.

Benjamin Franklin, around 1750, proposed that a single fluid flows from one body to another during rubbing. He called the body that gains fluid positively charged while the one loses fluid negatively charged. He mistakenly believed that glass gains the fluid during rubbing, thus positively charged.

Checkpoint 1

A

B

C

D AA

BD

D

C

Modern view Matter is made of atoms, which consists of a tiny nucleus of positive charge surrounded by electrons of negative charge. In the lowest energy state, atoms are neutral, i.e. with equal amount of negative and positive charge. Different atoms have different electron affinity. Thus the rubbing action between two materials might cause electrons to transfer from one to the other.

The SI unit of charge is the coulomb (C), which is defined in terms of electrical currents. It turns out that a coulomb is a large mount of charge. A typical charge acquired by a rubbed body is 10-8 C.

Quantization chargeIn 1909, R.A. Millikan measured the electrical charge through the drag force on tiny oil droplets and found that charge is quantized. The smallest charge is approximately

191.602 10e C

eq e pq e

Charge and mass

Conservation of chargeIn an isolated system, the total charge is constant.

Examples:

1. Franklin’s experiment(a) glass rod rubbed with silk.(b) person A received positive charge from the glass rod and person B received negative charge from the silk.(c) spark seen when either the knuckle of A or B was brought close to that of a neutral third person C.(d) spark not seen in the same situation as in (c) if A and B had touched each other beforehand. (e) Franklin concluded that equal amount of positive charge and negative charge were generated on rod and silk by rubbing and then transferred to A nd B respectively.

2. Na+ + Cl- NaCl3. n p + e + ˉˉ

Conductors and insulatorsAs early as 1729, an amateur named Stephen Gray discovered that most materials can be classified into two groups: conductors and insulators. Conductors, such as metals and ionic solutions, allow charge to flow freely; while insulators, such as wood, silk, and glass, do not.

Note that a third class of materials, called semiconductors such as silicon, germanium, and gallium arsenide, behave like insulators when they are pure and behave like metals when certain impurities are added in.

Charge relaxation time is about 10-12 s for copper, 2 s for glass, 4 103 s for amber, and 1010 s for polystyrene.

Charging by induction

Charging by induction

Coulomb’s law

Charles A. Coulomb (1736-1806)

Coulomb’s law

1 212 212

21

ˆkq q

F rr

q1

q1

q2

q2

21r̂

9 2 29.0 10 /k Nm C

Coulomb’s law

2 20

ˆ ˆ4

kqQ qQF r r

r r

12 2 20 8.854 10 /C Nm

Force on q :

r̂ : unit vector from Q to q

Coulomb’s law in Gaussian system

1 22

q qF

r

F : in units of dyne, or g cm/s2

R : in units of cm

q : in units of statcoulomb

91 3.00 10C statcoulomb

The magnitudes of electrostatic and gravitational force in a hydrogen atom

The electron and proton in a hydrogen atom are 0.53 10-10 m apart. Compare the electrostatic and gravitational force between them.

2

2

19 29

10 2

8

(1.6 10 )9.0 10

(0.53 10 )

8.2 10

E

eF k

r

N

N

2

31 2711

10 2

47

(9.11 10 1.67 10 )6.67 10

(0.53 10 )

3.6 10

e pG

m mF G

r

N

N

2

404.4 10

e pG

E

Gm mF

F ke

Exercise

Designing experiments to prove that the following expressions for the force between two point charges are incorrect.

21 22

kq qF

r 1 2

2

( )k q qF

r

Superposition of forces on electrical charges

1, 12 13 1...net nF F F F

1nF

: the force acting on the point charge 1 due to the presence of the point charge n.

Two shell theorems

1. A shell of uniform charge interacts with a point charge outside the shell as if all the shell’s charge were concentrated at its center.

2. There is no net force on a point charge inside the shell due to the shell’s uniform charge.

Note that the shell theorems are results of the fact:

2

1ˆF r

r

Spherical conductors

Question: Why there is no charge inside a spherical conductors and the net charge is distributed uniformly on the surface?

Some examplesThree point charges lie on the x-axis shown below. Both q1 = 15.0 μC and q2 = 6.0 μC are fixed in positions. Determine the position of q3

such that its net force is zero.

Some examples

Two identical small charge sphere, each having a mass of 3.0 10-2 kg and a charge of q. The length of each string is 0.15 m, and the angle is 5.0º. Find the magnitude of the charge q.

Change in equilibrium position and

frequency for small oscillation amplitudes

q q

kq

2

2

0 )(4

1

)21()1(4

1

)(4

10

22

2

02

2

0

CFqq

kFC )21(00CF

k

2

Change in equilibrium position :

Change in oscillation frequency for small amplitude ’ from

Restoring force:

)()2

1(

)()21(4

1)(

)(4

1

3

2

0

2

2

02

2

0

kkkq

kq

kq

3

3

)3(

)2(

Home work

Question ( 問題 ): 1, 2, 19

Exercise ( 練習題 ): 1, 7, 12

Problem ( 習題 ): 11, 19, 25, 26