# William M. Farmer
# 31 October 2010
#
# This is a solution for Lab 07: Minor Assignment 4.
#
# The grades file is assumed to have the following format (called
"courses.txt"):
#
# CHEM
1E03 3
9
# ENGINEER 1D04 4 12
# ENGINEER 1P03 3 10
# HISTORY 1B03 3
8
#1a.
#def
#
#
#
#
#
#
main():
print "This program illustrtes a chaotic function"
n=input("Enter the number of loops you would like to run: ")
x=input("Enter a number between 0 and 1: ")
for i in range(n):
x=2.0*x*(1x)
print x
#main ()
#Always remained cl
Engineer 1D04 Engineering Computation
Professor: Douglas G. Down
Office: ITB 126
Email: downd@mcmaster.ca
Office Hours: Tue, Thu 1:30 3:30
Wed Sept 7
Notes Week 1
Computing the development and use of computer hardware and software to:
Solve problems
Ma
Electrical Work and Power
Electrical Work and Power
I
+
Higher V1
Resistance R
I
Lower V2
Current I flows through a potential difference V
Follow a charge Q : at positive end, U1 = QV1
at negative end, U2 = QV2
P.E. Decreases:
U QV 0
The speed of the char
BiotSavart Law, Ampres Law
Fields and forces for current in straight wires
Ampres Law
Example 1: Long parallel
wires
L
a
b
I1
d
I2
Find force on current I1 in segment ab due to
current I2 (magnitude & direction)
(Take I1 = 20A, I2=30A, d=0.01m, L=1.5m)
Sources of Magnetic Fields
Besides magnetic poles, electric
currents create magnetic fields.
There are two ways of calculating B produced
by currents:
i) BiotSavart Law: Field of a current
element
(analogous to a point charge in
electrostatics).
ii) Ampr
More Examples of
BiotSavart &
Ampres Law
Recall:
ds
r
r2
BiotSavart Law:
o I
B
4
Amperes Law:
B
ds I
o
Quiz: A light, loose spiral spring carrying no
current is hung from a ceiling. When a switch is
closed so that a circuit exists in the spring, do t
Charged Particles in Electric
and
Magnetic Fields
Motion of charged particles
Lorentz Force
Examples: cyclotron, mass spectrometer
Recall:
F qE
F qv B
in an electric field
in a magnetic field
In general:
F qv B qE Lorentz Force
Magnetic Fields: F =
Magnetic Forces and Torques
Review:
Charged Particle in an external field:
F qv B
Straight wire of length L with current I
in a uniform external field B:
r
r r
F I LB
Note: L points in direction of positive current flow
Force on a currentcarrying wire
DC Circuits
Series and parallel rules for resistors
Kirchhoffs circuit rules
DC Circuits
Direct Current or DC: current always
flows in one direction.
For circuits containing only resistors and emfs the
current is always constant in time. Circuits containi
RC Circuits
 circuits in which the currents vary in time
 rate of charging a cap depends on C and R of circuit
 differential equations
Quiz:
After the switch is closed, the light from the bulb:
A) Is brightest just after the switch is closed, then
fade
Magnetism (3 weeks)
CHAPTER 29: Magnetic fields exert a force on
moving charges.
CHAPTER 30: Moving charges (currents) create
magnetic fields.
CHAPTERS 31, 32: Changing magnetic fields
create
(Induction)
electric fields.
Magnetic fields
Magnetic poles, fo
Current & Resistance

Current and current density
Ohms Law
Resistivity
Resistance
Electrical Current
CURRENT I is the amount of positive charge
flowing past a fixed point in the wire per unit
time :
dQ
I
dt
if charge dQ flows in time dt
Units: 1 ampere (
Capacitance (II)
Capacitors in circuits
Electrostatic potential energy
Capacitors in Circuits
Symbols:
Capacitor
Battery
Switch

+
or

+
Capacitor Combinations
Parallel
Series
A
B
A
B
What is the effective capacitance between A &
B?
A
B
Q
+Q
Ceff
c
Capacitance (II)
Capacitors in circuits
Electrostatic potential energy
Capacitors in Circuits
Symbols:
Capacitor
Battery
Switch

+
or

+
Capacitor Combinations
Parallel
Series
A
B
A
B
What is the effective capacitance between A &
B?
A
B
Q
+Q
Ceff
c
Current & Resistance

Current and current density
Ohms Law
Resistivity
Resistance
Electrical Current
CURRENT I is the amount of positive charge
flowing past a fixed point in the wire per unit
time :
dQ
I
dt
if charge dQ flows in time dt
Units: 1 ampere (
Capacitance (II)
Capacitors in circuits
Electrostatic potential energy
Capacitors in Circuits
Symbols:
Capacitor
Battery
Switch

+
or

+
Capacitor Combinations
Parallel
Series
A
B
A
B
What is the effective capacitance between A &
B?
A
B
Q
+Q
Ceff
c
Dielectric Materials
What is a dielectric material?
Dielectric materials consist of polar molecules which
are normally randomly oriented in the solid.
They are not conductors.
When a dielectric material is placed in an external
electric field, the polar
Dielectric Materials
What is a dielectric material?
Dielectric materials consist of polar molecules which
are normally randomly oriented in the solid.
They are not conductors.
When a dielectric material is placed in an external
electric field, the polar
Dielectric Materials
What is a dielectric material?
Dielectric materials consist of polar molecules which
are normally randomly oriented in the solid.
They are not conductors.
When a dielectric material is placed in an external
electric field, the polar
Dielectric Materials
What is a dielectric material?
Dielectric materials consist of polar molecules which
are normally randomly oriented in the solid.
They are not conductors.
When a dielectric material is placed in an external
electric field, the polar
Capacitance (Chapter 26)
Capacitance the property of a conductor or
set of conductors and insulators
to store electric charge
Capacitor an electronic component that has
the ability to store charge
Definition
Calculating Capacitance
Dielectrics and Dielect
Capacitance (Chapter 26)
Capacitance the property of a conductor or
set of conductors and insulators
to store electric charge
Capacitor an electronic component that has
the ability to store charge
Definition
Calculating Capacitance
Dielectrics and Dielect
Electric Potential (II)
Potential of a point charge
Potential of several point charges
Potential energy of a collection of charges
Review: Electric Potential
potentialenergy
V
charge
dV E ds
E x
dV
dx
Electric potential is not an absolute quantity. It i
Capacitance (Chapter 26)
Capacitance the property of a conductor or
set of conductors and insulators
to store electric charge
Capacitor an electronic component that has
the ability to store charge
Definition
Calculating Capacitance
Dielectrics and Dielect
Electric Potential (III)
 Fields
 Potential
 Conductors
Potential and Continuous Charge
Distributions
We can use two completely different methods:
dq
V ke
r
source
1. dV k dq ,
e
r
2.
Or, Find E from Gausss Law, then
dV E ds ,
B
VB VA E ds
A
Potential
Capacitance (Chapter 26)
Capacitance the property of a conductor or
set of conductors and insulators
to store electric charge
Capacitor an electronic component that has
the ability to store charge
Definition
Calculating Capacitance
Dielectrics and Dielect
Electric Potential (III)
 Fields
 Potential
 Conductors
Potential and Continuous Charge
Distributions
We can use two completely different methods:
dq
V ke
r
source
1. dV k dq ,
e
r
2.
Or, Find E from Gausss Law, then
dV E ds ,
B
VB VA E ds
A
Potential
Capacitance (Chapter 26)
Capacitance the property of a conductor or
set of conductors and insulators
to store electric charge
Capacitor an electronic component that has
the ability to store charge
Definition
Calculating Capacitance
Dielectrics and Dielect
Electric Potential (II)
Potential of a point charge
Potential of several point charges
Potential energy of a collection of charges
Review: Electric Potential
potentialenergy
V
charge
dV E ds
E x
dV
dx
Electric potential is not an absolute quantity. It i