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Ch26 Electric Charges and Forces

講者： 許永昌 老師

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ContentsDeveloping a Charge Model

Charges and MaterialsCharges

Atoms and ElectricityCharge Conservation and Charge diagram (P795)

Insulators and ConductorsCharging and DischargingCharge polarizationElectric Dipoles

Coulomb’s lawThe Field Model

Unit vector notation先講電，再講電力，最後講到電場。

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Action I ( 請預讀 P788~P790)

Purpose: Developing a Charge Model (課本P789 ~ P791 的圖很清楚 )

Objects: 2 Plastic taps Plastic rods + wool Glass rods + silk Small metal spheres

Action: (Easy,Exist & Charging) Quickly pulling a piece of tape cling to your hand:

New force? Long range force? (Hard, two types of charges) Rub plastic and glass rods with wool and silk.

How can you test whether or not an object is charged? (Easy, repulsive) Two pieces of tapes repulsive to each other. (Hard, attractive and charge transfer)

Charge two pith balls by touching them with charged plastic and glass rods. Make sure that they are charged. They will ___???______. How to charge a material? (1)….. (2)…… Which one is positive charged? Why?

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The conclusion thus far are:CHARGING PROCESSES:

Rubbing causes some objects to become charged.Charge can be transferred by contact.

TEST AND TWO KINDS OF CHARGES:A charged object attracts small neutral objects.

This is the test for charge.There are at least two different kinds of charge.

Like charges repel, different charges attract.

STOP TO THINK:Suppose there is a third type of charge. What test would

reveal that an object has this third charge? Charged? Attractive?

How to make sure that an object is neutral, positive, or negative?

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Action II ( 請預讀 P791~P792)

Purpose: Understand the concept of insulator and conductor.

Objects:One metal rodOne wood rodA small metal ballA pith ball

Action:由於不易產生大的靜電，以下的實驗不確定能否展示。As this figure shows, check whether the metal ball is

charged or not. Conclusion: Both insulators and conductors can be charged.

They differ in the mobility of the charge.

Charge diagram

Metal ballInsulator or

conductor

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Charge ( 請預讀 P793~P795)

Franklin: ( 簡單定義“正電” )A glass rod that has been rubbed with

silk is positively charged.Atoms and Electricity:

An atom consists of a very small and dense nucleus (diameter~10-14 m) surrounded by much less massive orbiting electrons. Electrons and Protons have charges of

opposite sign but exactly equal magnitude. Fundamental unit of charge:

e=1.6010-19 C. ( 小心，有的書本取負號。 )

Law of conservation of charge:Charge is neither created nor destroyed.

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The Micro/Macro ConnectionElectrons and Protons are the basic charges

of ordinary matter.Therefore, an object has charge q=Npe + Ne(-e).

Macroscopic: q Neutral: q=0.

STOP TO THINK: neutral 代表 no charge 嗎？Microscopic: Np, Ne, e.

Neutral atom (remove one electron) positive ion. Neutral atom (accommodate one electron)

negative ion.

Plastic rod is charged by rubbing with wool:Frictional charging via bond breaking works

well with large organic molecules as shown in Fig. 26.3.

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HomeworkStudent Workbook

26.126.426.9

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Insulators and ConductorsInsulators:

The electrons in the insulator are all tightly bound to the positive nuclei and not free to move around.

Conductors:There are something highly mobile inside

the conductors. The charges physically move are called the charge carriers. Metal:

Charge carriers: sea of electrons Ionic solutions:

Charge carriers: ions.

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Action III ( 請預讀 P797~P800)

Purpose:Get the feeling about polarization, discharging and

induction.Actions:

Polarization:

Discharging: The electric forced exerted by a charged tape will be more and

more weak as time pass. If it is contact with you or the earth, it discharges very fast.

Induction:

- - - - -

A piece of paper

Metal balls:Separate them while rod is held closer.

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Stop to ThinkHow to charge two identical metal spheres

with equal charges?How to charge two identical metal spheres

with opposite charges whose magnitudes are the same?

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HomeworkStudent Workbook

26.1126.1526.17

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Stop to ThinkPlot the force vectors upon these two

spheres. ( 小心，力怎麼畫關乎到誰當系統，假定以整個球當作一個系統好了。 )可利用 free-body diagram 與 interaction diagram 來想。

Do this experiment to confirm your thought.Different charge numbers.Different distances.

+++++ +

++

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Coulomb’s law( 請預讀 P800~P804)

Coulomb’s Law: ( 重點在於定出 force)If two charged particles having charges q1 and q2 are a

distance r apart, the particles exert forces on each other of magnitude

where k is called the electrostatic constant. These forces are an action/reaction pair, equal in magnitude and opposite in direction. Electrostatic constant: k=8.99109 Nm2/C2. Permittivity constant:

The forces are directed along the line joining the two particles. The forces are repulsive for two like charges and attractive for two opposite charges.

12 2 20

18.85 10 C / Nm .

4 k

1 2 1 21 on 2 2 on 1 2 2

0

.4

k q q q qF F

r r

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Using Coulomb’s Law仔細看，其實很有限：

Coulomb’s law applies only to point charges.Coulomb’s law applies only to electrostatic.Electric forces, like other forces, can be

superimposed.Exercise: ( 千萬別亂用屏蔽 “ screening” 的概

念 )Draw the individual and net force vectors on

the right one:

Draw the individual and net force vectors on charge B:

-2 2 -12 1

+

+ -

+1nC

(B) +1nC -2nC

5cm-

+ -

-1nC

(B) +1nC -2nC

5cm

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HomeworkStudent Workbook

26.2026.24

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A Problem of Coulomb’s Law and Newton’s Law of GravityLogical deduction:

Objects: One source charge and one test charge.

Situations: 1. If both source and test charges are at rest, the force pairs

no doubt obey Coulomb’s Law. 2. If the source charge suddenly starts moving, as shown by

arrow. In response, the force vector on the test charge must pivot to follow the source charge. Does this happen instantly? Or is there some delay?

Neither Coulomb’s Law nor Newton’s Law of gravity is dependent on time. instantly.

However, How about the case of the distance between these two particles is about 1,000,000 light years? some delay?

source test on t 0sF t

t=0

t=t’

on t 'sF t t

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The Field Model ( 請預讀 P805~P810)

Faraday’s Concept:The source particle alters the space around it.

(The space around the source particle is altered to create the electric field.)

The test particle then responds to the altered space. The interaction between the test particle and this

alternation of space is a local interaction rather like a contact force.

In classical electrodynamics, you will find that people use MAXWELL EQUATION to describe the EM field generated by the source and the LORENTZ FORCE to describe the interaction between EM field and the test charge.

Newtonian view

Faraday’s View:(see animation)

FA on B:

AB

A B

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The Electric FieldThree basic concepts:

1. The field exists at all points in space, even though diagrams may show a few illustrative vectors.

2. The test charge measures the field. (☆)Test charge also creates an electric field. But charges don’t

exert forces on themselves, so the test charge is measuring only the electric field of other charges.

3. The field at each point in space is a vector.

For single particle source:

Unit vector:

on attestq r

test

FE r

q

2

02 2

direction0 0

magnitude

14 1 1

ˆ, away from , away from .4 4

test

test

kqq

r kq kqE r q q r

q r r

ˆ .r

rr

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ExercisesQ1: Plot the electric field created by these

two particles.

Q2: Which one is the possible electric field?

+ +

(a) (b)

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HomeworkStudent Workbook

26.2826.29

Student Textbook26.5826.59自己寫 Terms and Notation.