Andres La Rosa
Portland State University
Lecture Notes
PH-212
ELECTROMAGNETISM
magnets in motion
produce current
1820 Oersted
charges
in motion
Charges
in motion
produces
magnetism magnetism
produce
moving
magnet
bulb
wire
switch
Electrostatic
-
+
ELECTRICITY
ELECTRICITY
MAGNETISM
MAGNETISM
ELECTROMAGNETISM
ELECTROMAGNETISM
Maxwell
equations
Maxwell
equations
predicts that
light is an electromagnetic
wave
Unification
theories
Einstein
Electromagnetism
Electricity
Magnetism
Gravitation
Classical Mechanics
(Newton's laws
Electricity
Magnetism
Electromagnetism
Quantum Mechanics
Quantum
Electrodynamics
The Electric Charge
(-)
(+)
The terms "positive" and "negative" are arbitrary
Typically atoms are neutral; i. e.
-
Charges of the same sign
repeal each other
Negative
Charges of opposite sign
attract each other
Negative
Negative
+
Positive
MATERIALS
Most solids are crystalline, i.e. its atoms are arranged in is
a structural periodic array.
The crystalline arrangement is referred to as a crystal
lattice
Nucleus
Electrons
. . . . . . .
. . . . . . .
. . . . . . .
. . . . . . .
CRYSTAL
LATTICE
CONDUCTORS
Materials that contain “free" electrons)
Crystal's
energy level
Atom's
energy level
Electrons in the crystal's
energy levels are “free”
to wander across the metal
What happens when a voltage is applied across a metal?
The "free" electrons travel across the crystal, jumping from atom to
atom. On average, the move with a velocity termed "drift velocity"
Open question: Can you estimate the value of the electrons' drift velocity
in a metal?
INSULATORS
Materials that do not contain “free" electrons
Crystal's
energy level
Atom's
energy level
Insulator
Material with no “free"
electrons available
What happens when a voltage is applied across the
insulator material?
+V ( Voltage from a
battery )
No macroscopic translational
motion of charges
At most, charges
+
+
+
re-distribute inside
Positive charges position to the left side of the atom,
each atom
while
negative charges position to the right side of the atom.
The electric charge is quantized
Charge induction
Example
Example
Hollow
metallic
shell
+
+
+ induced +
+
negative charges
Initial:
Neutral shell
induced positive
charges
+q2
+
-- - -
- +
-q1
+Q
- - - -+
-
+
+
+
+ a point
Charge distribution after
harge +Q is placed at the
center of the shell,
The electric charge is conserved
Example: Charge induction and the protection of
electronic equipment
Metallic shell
Electronic
circuit
Atoms that lost
their free electrons
COULOMB'S LAW
(2)
(1)
q1 (+)
q2 (-)
(3)
What is the orientation of the
electrical; force acting on the
charge q2?
Could it be (1), (2), (3), or else?
q2 (-)
Answer :
q1 (+)
Quantitative aspect of the
Coulomb's law
We know that
What is new is the
following
r
r: distance between the
charges 1 and 2
Coulomb's Law
Definition of the unit charge: The COULOMB
When the distance between two point charges (of equal
magnitude) is 1 meter,
q
q
(+)
F
(+)
1m
and they repeal with a force of magnitude equal to
Then we say that each charge has an electrical
charge equal to
q = 1 Coulomb
When q1 = q2= 1 Coulomb and they are
apart a distance d= 1meter, the electrostatic
force they exert to each other is 9 x 109
Newtons.
FORCE is a VECTOR
magnitude
orientation
Given a line, let's find a UNIT
VECTOR parallel to that line
RECIPE
1 Pick up any two points A and B along the line
2 Evaluate
the
vector
Evaluate
the
magnitude of
3 The
vector
will be a unit vector
oriented along the specified line. That is,
Example.
Calculate the electrostatic force F21 exerted on the charge
q2 due to the charge q1.
cm
cm
a) Evaluation of the magnitude of the force
F= 180 Newtons
b) Evaluation of the orientation of the force
Strategy
F
Find the proper
UNIT VECTOR
The 4 forces in nature
Checkpoint 1 (page 564)
Repeal or attract
each other ?
About the notation of forces
About evaluating the force components: When to use SIN or COS
The principle of superposition
if Q2 were not present.
+ qo
if Q1 were not present
+ qo
Answer:
METHOD-1 Finding the total force
acting on a point-charge
Y (cm)
What is the total
force acting on
qo?
qo
q2
q1
X (cm)
Magnitude
Unit
vector
Magnitude
How to evaluate the proper unit vector?
Y (cm)
qo
q1
q2
X (cm)
Answer
For example :
5 cm
(no units)
Therefore,
We can apply a similar procedure to calculate
:
Y (cm)
= Fo2
qo
q2
q1
-3
-2
-1 0
1
2
3
X (cm)
How to find
R2 is a vector that start at the
position of qo and ends at the
position of q2.
5 cm
F02
F02
Newtons
Newtons
METHOD-2 Finding the total force
acting on a point-charge
Exploit symmetry, if applicable
Y (cm)
qo
q2
q1
X (cm)
F2
θ
4
q1
θ
F1
qo
q2
Y (cm)
qo
q1
q2
X (cm)
Y (cm)
θ
F1
qo
q1
θ
F2
q2
X (cm)
What to do when the charge distribution (Q) lacks
symmetry?
Method:
Break down the total charge into
small point-charges (see mesh in the
figure).
Evaluate the interaction between q
and the different small charges.
Then add up all those individual
forces