Chapter 5 (part-1) Electric Charge In this chapter we will introduce a new property of matter known as “electric charge” (symbol q ). We will explore the charge of atomic constituents.

Moreover, we will describe the following properties of charge:

- Electic charge - Forces among two charges (Coulomb’s law) - Charge quantization - Charge conservation

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Global Electric Circuit Global Electric Circuit 1.  The Earth’s surface has a negative charge

with respect to the air above. Some of this charge originates in the Earth’s core which is radioactive.

2.  This charge can move about because the ground is electrically conductive.

3.  The ionosphere is filled with a positive ions and charged particulates. Cosmic rays contribute heavily to the ionization.

4.  Electrons in the ionosphere slowly find their way to the Earh’s surface through lightning flashes and airway conduction.

5.  The ground charge can leak upward in water vapor forming rain clouds.

6.  The lower cloud layer will be negative with respect to upper positive cloudl. The ground below becomes positively charged.

+++++ ++ + Cloud --------- +++++ Ground 7. The cloud’s negative charge layer may discharge to ground in a lightning bolt when the electric field becomes too high.

Experiments on charged objects showed that:

1.  Same sign charges repel each other (fig.a)

2.  Opposite sign charges attract each other (fig.b)

•  Charges of the same sign repel each other.

•  Charges of opposite sign attract each other

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Empirically it was known since ancient times that if amber is rubbed on cloth, it acquires the property of attracting light objects such as feathers. This phenomenon was attributed to a new property of matter called “electric charge”. (electron is the Greek name for amber) More experiments show that they are two distinct type of electric charge positive and negative.

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When the positive terminal and the negative terminal of a battery are connected to a length of copper wire, the electrons are attracted towards the positive terminal of the battery forming a current of electrons each carrying a charge of -1.6 X 10-19 Coulombs. The first true battery was invented by the Italian physicist Alessandro Volta in 1800 with Cu and Zn.

I(A)= dqdt(C / s)

I (Amps) q(Coulombs)1e =1.602x10−19C1C =6.24x1018eOneCoulombisthechargethatflowsinacircuitinonesecond.

Zn Cu

Electric Current

Investigations of the structure of atoms by Ernest Rutherford at the beginning of the 20th century revealed how matter is organized and also identified that charge of its constituents.

Atoms consist of electrons and the nucleus. Atoms have sizes ~ 5x10-10 m Nuclei have sizes ~ 5x10-15 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)

Thus electric charge is a fundamental property of the elementary particles (electrons, protons, neutrons) out of which atoms are made of. 5

- electrons

+ + protons

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Conductors and Insulators

An insulator is a material that does not allow electricity to easily pass. The electrons in the atoms of insulators do not freely move from atom to atom. There is more resistance to the movement of the electrons. Rubber, plastics, wood and paper are examples of insulators

A conductor is a material that allows electricity to easily pass. There are free valence electrons which move easily though the material. There is less resistance to the movement of the electrons. Aluminium, copper, gold, water and people are examples of conductors.

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Charging by friction Different atoms/molecules have different “electron affinity”. Suppose that a rubber rod is rubbed with a sample of animal fur. During the rubbing process, the atoms of the rubber are forced into close proximity with the atoms of the animal fur. The electron clouds of the two types of atoms are pressed together and are brought closer to the nuclei of the other atoms. The protons in the atoms of one material begin to interact with the electrons present on the other material. The atoms of rubber begin to take electrons from the atoms of animal fur. When the rubbing has ceased, the two objects have become charged. Fur(+positive) Plastic Rod(-negative)

http://www.ipodphysics.com/forces-field-create-a-charge.php

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Conductor

Insulator Insulator

If a + rod is brought near a conductor charges can move to balance the forces. There will be a net attractive force.

If a + or - rod is brought near an insulator the insulator polarizes. There will be a net attractive force albeit weaker.

Mass and charge of atomic constituents

Neutron (n) : Mass m = 1.675x10-27 kg ; Charge q = 0

Proton (p) : Mass m = 1.673x10-27 kg ; Charge q = +1.602 x10-19 C

Electron (e) : Mass m = 9.11x10-31 kg ; Charge q = -1.602 x10-19 C

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

Note 2: Atoms are electrically neutral. The number of electrons is equal to the number of protons. This number is known as “ 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

238 The atomic number Z = 92 defines the nucleus as that of a Uranium atom

92235U 92

238U

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isotopes

silk

glass rod

silk

glass rod

- - - -

+ +

+ +

Conservation of Charge

Consider a glass rod and a piece of silk cloth (both uncharged) shown in the upper figure. If we rub the glass rod with the silk cloth we know that positive charge appears on the rod (see lower figure). At the same time an equal amount of negative charge appears on the silk cloth, so that the net rod-cloth charge is actually zero. This suggests that rubbing does not create charge but only transfers it from one body to the other, thus upsetting the electrical neutrality of each body. Charge conservation can be summarized as follows: In any process the charge at the beginning equals the charge at the end of the process.

Net charge before = Net charge after

i fQ Q=10

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Quantization of Charge Q = ne The Millikan oil drop experiment was performed by Robert A. Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron). The experiment took place in the Ryerson Physical Laboratory at the University of Chicago. Their data showed that the static charge on oil droplets only came in multiples of the fundamental electric charge e=1.6 x 10 -19 C.

Coulomb's lawConsider two charges q1 and q2 placed at a distance r.

The two charges exert a force on each other that has thefollowing characteristics: 1. The force acts along the line connecting the two charges2. The force is attractive for charges of opposite sign The force is repulsive for charges of the same sign3. The magnitude of the force, known as Coulomb

force is given by the equation: F = 14πεo

q1 q2

r 2

The constant εo is known as permitivity constant

εo =8.85×10-12 C 2 /N ⋅m2

The Coulomb force has the same form as Newton'sgravitational force. The two differ in one aspect:The gravitational force is always attractive. Coulomb's force on the other hand can be eitherattractive or repulsive depending on the signof the charges involved

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!F12 =

14πεo

q1 q2

r 2 r

ke =1

4πεo

= 8.9x109 N − m2

C 2

Units of Charge (Coulomb)The unit of charge in the SI unit system is the "Coulomb" (symbol C)In principle we could use Coulomb's law for two equal charges q as follows:Place the two charges at a distance r = 1m. q = 1 C

F = 14πεo

q2

r 2 → F = 14× 3.14×8.85×10-12

12

12 = 8.99×109 N

For practical reasons that have to do with the accuracy of the definition, the electric current is used instead. The electric current i is defined by the equation

i = dqdt

i.e. the is the amount of charge that flows though any cross section

of the wire per unit time. The unit of current in SIis the Amprere (symbol A) and it can be defined very accurately.

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For example the net force !F1 exerted on q1 by q2 and q3 is equal to:

!F1 =

!F12 +

!F13

Here !F12 and

!F13 are the forces exerted on q1 by q2 and q3, respectively.

In general the force exerted on q1 by n charges is given by the equation:!F1 =

!F12 +

!F13 +

!F14 + ...+

!F1n =

!F1i

i=2

n

∑One must remember that

!F12 ,

!F13 , ...are vectors

and thus we must use vector addition.

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The net electric force exerted by a group ofcharges is equal to the vector sum of the contributionfrom each charge.

Coulomb's law and the Principle of Superposition

!Fq0

=q0

4πε0

qi

r 2 ri∑ po int charges

!Fq0

=q0

4πε0

dqr 2∫ r continuous charge

distribution

m1 m2 r

F1

m2 m1

F1 = G

m1m2

r 2

Q1 Q2 r

F1

Q2 Q1

1 21 2

1 4 o

Q QF

rπε= F12 = 0

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Shell TheoremThe gravitational force that a uniform shell of mass m2 exerts a particle of mass m1

that is outside the shell is given the the equation: F1 = Gm1m2

r 2

It is as if the shell's mass m2 were all concentrated at the shell center.

If m1 is inside the shell, the net force exerted by m2 is zero.

Because of the similarity between Newton's gravitational law and Coulom's law,the same is true for the electric force exerted by a spherical shell of charge Q2

on a point charge Q1. If Q1 is outside the shell then the force F1 exerted by Q2 is:

F1 =1

4πεo

Q1 Q2

r 2 If Q1 is inside the shell then the force F1 = 0

F12 = 0

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!F21 =0i +

k(3e)(2e)d2

j =0i + 6ke2

d2j

!F23 =

−k(3e)(5e)(2d)2 i +0 j = −15ke2

4d2 i +0 j

!Fnet =

!F21 +!F23 = −

15ke24d2 i + 6ke

2

d2j

!Fnet = (−2.16x10−14 , +3.46x10−14 )N| !Fnet |= Fx

2 +Fy2 = 4.07x10−14N

ϕ = tan−1(FyFx)= −58o

-3e

-5e

+2e

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1 2 F2x

F2y

ke =1

4πε0=8.99×109 N·m2·C −2

d =2(0.5m sin(5o))=0.087m

Fx2 =kQ2

d2Coulomb force on ball-2

Fy2 =mg Gravity force on ball-2

tan(θ )=Fx2Fy2

= kQ2

mgd2

Q = mgd2tan(5o)k

= (0.005kg)(9.8N /kg)(0.087m)2(0.087)8.99×109N·m2·C −2

Q =6.0x10−8C The sign is either + or -?

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1 2

3 4

!F21 = +

kq2

a2i

!F41 = −

kq2

a2j

!F31 =

kq2

( 2a)2(+ 1

2i −12 j)

!F =!F21 +

!F41 +

!F31

!F = (kq

2

a2+ 1

2kq2

2a2 )i +(−kq2

a2− 1

2kq2

2a2 ) j

!F = (kq

2

a2+ 1

2kq2

2a2 )i −(kq2

a2+ 1

2kq2

2a2 ) j

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45o r = 1

2i + 1

2j1

130o

r = 32 i + 12 j

3

1 2 2

r = cosθ i + sinθ jy x2 + y2

x

θ

UnitVectorrTheunitvectorr pointsinthedirectionof!randhasunitmagnitude.

r =!r| !r | = x i + y j

x2 + y2= x

x2 + y2i + y

x2 + y2j= cosθ i + sinθ j

r = cosθ i + sinθ j

r

r

r

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STOP HERE