Electromagnetism & OpticsPHYS241

Lecture Section 03

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Textbook: Fundamentals of Physics, 8th Edition, by Halliday, Resnick and Walker

Name: Dr. Kofi Agyeman

Room: 2105

Email :kagyeman@pi.ac.ae

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Chapter 21: Electric Charge21-1

1. Computers, TV, radio, telecommunications, lighting, etc,…..

2. Atoms, molecules, lightning, auroras etc,………….

3. Electromagnetism is a study of the combination of electric and magnetic phenomena

4. Greek philosophers were the first to try and understand the science of electricity and magnetism

5. Important names in history of electricity and magnetism include Oersted, Faraday, Maxwell, etc.

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Electric charge21-2

Some facts and observations include:

• Sparks, static cling (see Applet)

• Charge is an intrinsic property of all matter

• There are two kinds of charge, positive and negative

• Bodies are said to be neutral if they do not carry excess charge – they have equal amounts of positive and negative charges

• Bodies are said to be charged if they carry net charge

• Charges with the same sign repel each other; charges with opposite sign attract each other

In Benjamin Franklin’s day (18th century) it was assumed that electric charge is some type of weightless continuous fluid. Investigations of the structure of atoms by Ernest Rutherford at the beginning of the 20th century revealed how matter is organized and also identified the charges of its constituents.

Atoms consist of electrons and the nucleus.

Atoms have sizes 510-10 m.

Nuclei have sizes 510-15 m.

The nucleus itself consists of two types of particles:

protons and neutrons.

The electrons are negatively charged. The protons are positively charged. The neutrons are neutral (zero charge).

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Thus electric charge is a fundamental property of the elementary particles (electrons, protons, neutrons) out of which atoms are made.

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Mass and Charge of Atomic Constituents

Neutron (n) : Mass m = 1.67510-27 kg; Charge q = 0

Proton (p) : Mass m = 1.67310-27 kg; Charge q = +1.60210-19 C

Electron (e) : Mass m = 9.1110-31 kg; Charge q = -1.60210-19 C

Note 1: We use the symbols “- e” and “+e” for the electron and proton charge, respectively. This is known as the elementary charge.

Note 2: Normally atoms are electrically neutral. The number of electrons is equal to the number of protons. This number is known as the “ atomic number ” (symbol: Z). The chemical properties of atoms are determined exclusively by Z.

Note 3: The sum of the number of protons and the number of neutrons is known as the “ mass number ” (symbol: A).

Notation: Z = 92 = number of protons/electrons A = 235 = number of protons + neutrons

The atomic number Z = 92 defines the nucleus as that of a uranium atom.

23592 U

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APPLET – ‘Travoltage’ (PHET)

http://phet.colorado.edu/web-pages/simulations-base.html

Glass rubbed with silk leaves a positive charge on the glass

Plastic rubbed with fur leaves a negative charge on the plastic

Uses of attraction and repulsion in industry include:

• Photocopiers

• Ink-jet printers

• Spray painting

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Conductors and InsulatorsMaterials can be classified according to their ability of charge to move through them.

Conductors: charge can move relatively freely through conductors. Examples include metals such as copper, silver, gold, human body, tap water

Excess charge on a conductor is distributed so that the net force on any charge is zero

21-3

Insulators (or nonconductors): are materials through which charge cannot move freely. Examples include rubber, paper, glass

Any excess charge on an insulator does not move far from the place where it is deposited

Semiconductors: are materials that are intermediate between conductors and insulators. Examples include silicon and germanium

Superconductors are materials through which charge can move without resistance (or hindrance); examples include Pb, Sn, etc

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Charging objects

• Charging by friction (rubbing) – already discussed as the method for charging insulators

• Charging by conduction – demonstrate with electroscope

• Charging by induction – demonstrate with electroscope

OR

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Polarization

-OHP

-Demo with comb/paper

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+

+

+

+

+

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Example of charge by induction in medical practice

Bacterial contamination during surgery

As part of your reading, attempt the Checkpoint questions at the end of some sections. An example follows:

CP 1A, B, and D are charged plastic plates and C is an electrically neutral copper plate. The electrostatic forces between the pairs of plates are shown for 3 of the pairs. For the remaining two pairs, do the plates repel or attract each other?

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Coulomb’s Law

For two charges q1 and q2 separated by distance r, the magnitude of the electrostatic force exerted by one charge on the other is given by:

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1 22

|| ||q qF kr

21-4

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In words:

The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Note: 12 21F F

12 21| | | |F F

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In vector notation:

1q 2q

1q 2q

If q1 and q2 are both positive (or both negative), then is in the same direction as

If q1 and q2 have opposite signs, then is in the opposite direction to

21F

21F

21F

21F

r̂

r̂

r̂

r̂

1 221 2

ˆq q

F k rr

Note the close similarity between the form of Coulomb’s Law and Newton’s equation for the gravitational force between two particles of masses m1 and m2 separated by distance r

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where G is the gravitational constant

Read page 566 carefully and list the similarities and differences between the two laws

For Coulomb’s Law, the constant of proportionality, k is called the electrostatic constant

The SI unit of electric charge is called the coulomb (1 C), defined such that: 1 C = (1 A)(1 s) (More in Chap 26)

1 22

ˆmm

F G rr

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The unit of charge in the SI unit system is the "coulomb"

In principle we could use Coulomb's law for two equal charges as follows:

Place the two charges at a distance

(symbol C )

.

=

q

r

Units of Charge

9

0

2 29

2 -12 20

11 . = 1 C if 8.99 10 N:

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1 1 1 8.99 10 N

4 4 3.14 8.85 10 1

For practical reasons that have to do with the accuracy of the definition, the

electric current is used instead. The

m q F

qF F

r

electric current in the circuit of the figure

is defined by the equation i.e., the amount of charge that flows

through any cross section of the wire per unit time. The unit of current in S

,

I

i

dqidt

i

s the ampere and it can be defined very acc(symbo uratel A) ly.

If we solve the equation above for we get .

Thus if a current = 1A flows through the circuit,

a charge = 1C passes through any cross section

of the wire in one second.

dq dq idt

i

q

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• In SI units the constant k is:

• For historical reasons the electrostatic constant k is usually written as:

• where ε0 is another constant called the permittivity

constant. Its value is

9 2 28.99 x10 . /k N m C

12 2 20

8.85x10 / .C N m

• It is often instructive to compare electrostatic and gravitational forces. Use example of two protons separated by distance d to show that (see Sample problem 21.4)

• Hence we can often neglect gravitational forces when compared to electrostatic forces

0

1

4k

3610el

grav

F

F

Principle of superposition

• If we have n charged particles, they interact independently in pairs, and the force on any one charge is the vector sum:

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1 12 13 14 15 1net nF F F F F F

This is also true of gravitational forces

What happens when we have more that two charges?

Consider a charge configuration of more than two charges. The net electric force on the charge at P is then obtained using the superposition principle.

Q2 -

Q1 +

Q3 -

P

Q4

+ 41F42F

43F

4 42 43 41netF F F F

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A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all shell’s charge were concentrated at its center

Q

q qQ

Q q

If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell

Excess charge on spherical conducting shell is spread uniformly over the surface of the sphere

Qq

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R = 0.0200 m ;q1= 1.60 x 10-19 C

q2 = 3.2 x 10-19 C24

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2412

1.15x10 N

ˆ(1.15x10 N)i

F

F

2413

2413

2.05x10 N

ˆ(2.05x10 N)i

F

F

24 241, 12 13

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ˆ ˆ(1.15 x 10 )i (2.05 x 10 )i

ˆ(9.00 x 10 )i

netF F F N N

N

Sample Problem 21.1

Study the rest of the sample problem!

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, 1, 2, 3,.......q ne n e = 1.602 x 10-19 C

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The electronic charge e is the elementary charge. Note that the proton and neutron are made up of quarks which have fractional charges like

However these fractional charges cannot exist individually

1 2

3 3eand e

• Matter is discrete in the sense that it is composed of atoms and molecules.

• Electric charge in a body is discrete, a multiple of the elementary charge, e

Charge is Quantized

We say charge is quantized

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( )( )

e e Annihilatione e Pair production

21-6 Charge is conserved

Charge is not created or destroyed. It is merely transferred from one body to another or from one place in a body to another part of the same body

Examples:

238 234 492 90 2 ( )U Th He Radioactive decay