PHYS 2421
Fields and Waves
Instructor: Jorge A. López
Office: PSCI 209 A, Phone: 747-7528
Textbook: University Physics 11e, Young and Freedman
Chapter 21:
Electric Charge and Electric Field
21.1 Electric charge
21.2 Conductors insulators, and induced charge
21.3 Coulomb’s law
21.4 Electric field and electric forces
21.5 Electric field calculations
21.6 Electric field lines
21.7 Electric dipoles
Section 21.1: Electric charge
Amber can attract stuff
Section 21.1: Electric charge
Examples of electrostatics
Section 21.1: Electric charge
Benjamin Franklin (1706-1790) figured out
 There were two kinds of “charges”
 When a charge is produced on one body, an
equal but opposite charge is produced on the
other body
 He arbitrarily call them positive and negative.
 Equal charges repel
 Unequal charges attract
Section 21.1: Electric charge
Electric charge and the structure of matter
Subatomic particles are the
source of electricity
 Charge of e = - charge of p
 Charge of e is a unit of charge

Electrons can be
removed from
atoms
 “Ions” are atoms
with excess charge

Section 21.1: Electric charge
Summary of Section 21.1
• There are two kinds of charges: + and –
• There is charge conservation
• Equal charges repel, unequal charges attract
• Subatomic particles are the source of electricity
• Charge of e = - charge of p
• Charge of e is a unit of charge
• Electrons can be removed from atoms
• “Ions” are atoms with excess charge
Section 21.2: Conductors,
insulators and induced charge
Copper atom, 29 electrons
Conduction
electron
Piece of copper metal
 Electrons can hop from atom to atom
 Process requires a force
 Protons are fixed with material

Path of electron in iron (2 valence electrons)
Section 21.2: Conductors, insulators and induced charge
Insulators can be charged by friction
“Conductors” can
conduct electrons
 Insulators cannot
conduct
 Semiconductors are
in between

Conductors must
be charged in
isolation
Section 21.2: Conductors, insulators and induced charge
Charging by induction
Section 21.2: Conductors, insulators and induced charge
Charging by induction
Section 21.2: Conductors, insulators and induced charge
Attraction of neutral insulators by polarization
Polarization:
Section 21.2: Conductors, insulators and induced charge
Summary of Section 21.2
• Electrons can hop from atom to atom in conductors
• Insulators cannot conduct
• Protons are fixed with material
• Insulators get charged by friction
• Charging by induction
• Attraction of neutral insulators by polarization
Homework for Section 21.2
• Question 21.4 (11th Ed) or 21.5 (12th Ed)
• Question 21.9 or 21.10 (12th Ed)
Section 21.3: Coulomb’s law
Electric forces are:
 Inversely proportional to square of distance
 Proportional to magnitude of charges
 In direction of charges
q1
F
F
r
q1q2
F
2
r
Units:
 F in Newtons
 r in meters
 Units of q1 and q2 ?
q2
Charles Agustine Coulomb
(1736-1806)
Section 21.3: Coulomb’s law
• Use constant of proportionality k
• Derive unit of charge from unit of electric current
F =k
q1q2
(21.1)
2
r
k  8.988 109 N×m2 /C2 , q in Coulombs
1Coulomb = charge in 6 1018 electrons
To simplify future formulas: k =
1
4 0
;
 0  8.854 1012 C2 /(N×m2 )= "permittivity" of free space
Section 21.3: Coulomb’s law
neutron 0
proton + +
0
 particle
2
q
Electric force
4 0 r 2
2
m
Gravitational force Fg  G
r2
Fe 
1
q  2e  3.2 10 19 C
m  6.64 10 27 kg
q
q
+
+
r
Fe
1 q2
9.0 109 N  m 2 / C 2
(3.2 10 19 C) 2


2
Fg 4 0G m
6.67 10 11 N  m 2 / kg 2 (6.64 10 27 kg) 2
 3.11035 Gravitational force << electric force!
Section 21.3: Coulomb’s law
q1  25 nC, q2  75 nC


F1 on 2   F2 on 1
+
F2 on 1
F1 on 2 
1
r
F1 on 2
r  3.0 cm
q1q2
4 0 r 2
(25 10 9 C)(75 10-9 C)
 (9.0 10 N  m / C )
(0.030 m) 2
 0.019 N
 F2 on 1
9
2
2
Section 21.3: Coulomb’s law
Section 21.3: Coulomb’s law
Section 21.3: Coulomb’s law
Summary of Section 21.3
Electric forces
•inversely proportional to square of distance
•proportional to magnitude of charges
•Forces are to be added vectorially
F =k
q1q2
r2
, k  8.988 109 N×m2 /C2
Homework for Section 21.3
• Problem 21.21 (11th Ed) or 21.21 (12th Ed)
• Problem 21.17 (11th Ed) or 21.17 (12th Ed)
Section 21.4:
Electric field and electric forces
A charge affects another
charge at a distance,
imagine a two-step process:
1. Charge affects space
around it
2. Space affects charges in it
The effect of a charge on
the space is known as the
creation of a “field”
What is a field?
Section 21.4: Electric field and electric forces
Example of a scalar field:
Temperature
Magnitude exists everywhere
Example of a vector field:
Wind velocity
Magnitude and direction
exist everywhere
Section 21.4: Electric field and electric forces
For the electric field . . .
The electric field is the electric
force per unit charge E  F
q0
The force can be obtained by
F = q0 E
Section 21.4: Electric field and electric forces
Rules for drawing electric field lines
• Lines originate on a positive charge
• Lines end on a negative charge
• The number of lines is proportional to
the magnitude of the charge.
• Field lines cannot cross each other.
• The line must be perpendicular to the
surface of the charge
Electric field is given by E = k q rˆ
2
r
The unit vector r̂ points radially away from the charge
Section 21.4: Electric field and electric forces
Section 21.4: Electric field and electric forces
Section 21.4: Electric field and electric forces
Section 21.4: Electric field and electric forces
Ex. 21.8: An electron trajectory
Section 21.4: Electric field and electric forces
Summary of Section 21.4
• The electric field is the electric force per unit charge
F
E
q0
q
E = k 2 rˆ
r
Electric field points radially away from positive charges and
toward negative charges
Homework for Section 21.4
• Problem 21.27 (11th Ed) or 21.29 (12th Ed)
• Problem 21.32 (11th Ed) or 21.34 (12th Ed)