ECE106 Study Guide - Fall 2018, Comprehensive Midterm Notes - Electric Field, Euclidean Vector, Gauss'S Law
12 Oct 2018
School
Department
Course
Professor
ECE106
MIDTERM EXAM
STUDY GUIDE
Fall 2018
1
∂t
1
Introduction
This course covers electricity and magnetism. At the heart of the topics are the four famous
equations known as the Maxwell’s equations,
∇
.
D
˙
=
ρ
Gauss
la
w
(1.1)
∇
.
B
˙
=
0
No
magnetic
monop
oles
(1.2)
∇
×
H
˙
=
J
˙
+
∂
D
˙
∂t
Ampere’s law (1.3)
∇
×
E
˙
=
−
∂
B
˙
Faraday’s law (1.4)
At the end of this course you will understand what each of these equations stand for. These equations
would lead to the unification of electromagnetism with light and are responsible to explain many
wonderful phenomena you see in daily life.
Warning
: This course is extremely math intensive and it would build upon the materials taught
during the lectures. So you have to keep up or else you will be lost. Even sparing a week will put
you in trouble. We would try to explain phenomena seen in life and connect them to electricity
and magnetism. For example, lightening, magnetic levitation, northern lights, why is the sky blue,
rainbows, etc. Our goal is to make you see through these equations, to make you see and understand
the beauty around you and in doing so fell in love with physics. In general, the lectures will not be
a repeat of your book but will be complementary to the material. The notes are accessible online
but they do not stand on their own. Please remember that they should be used in combination with
the lectures.
1
Electrostatics
1.1
Introduction - What holds the world together?
Electricity and magnetism is all around us. Some examples are lights, television, computers,
calculators, cell phones and etc. Light itself is an electromagnetic phenomena as radio waves are.
The colors of the rainbows in the sky is due to electricity. Cars, planes and trains can only run
because of electricity. Even horses need electricity due to the fact that muscle contraction is caused
by electrical signals. In fact your nervous system is driven by electricity and you may not be able
to think if there was no electricity.
A modern picture of an atom is illustrated in Fig. 2.1. Electrons are in a cloud around the core
(nucleus) and they are negatively charged. The nucleus includes of protons which are positively
charged ,
p
+
, and neutrons which are neutral. Their masses are,
mp ≈ mn ≈ 1.7 × 10−27kg (2.1)
me ≈ 9.1 × 10−31kg (2.2)
For a neutral atom, the number of electrons and protons are the same meaning the cumulative charge
of the hole atom results in zero. Thus, there are two types of charges which are the positive and
the negative charges. Protons are very difficult to remove from an atom but electrons are different.
Adding an extra electron would result in a negative ion where as removing an electron would result
in a positive ion. Therefore, charge can be redistributed but never destroyed.
In 600 B.C., people knew that if you rub amber, it attracts pieces of dry leaves. The Greek
word for amber is “electron”. In the mid-sixteenth century, when people got bored at parties, they
would rub amber jewelry and stroke frogs with it causing them to jump in despair due to static
electricity shock. In eighteenth century, it was discovered that there are two types of electricity
when you rub amber versus glass. It was also discovered that the same types repelled each other
while the opposites attracted each other. Benjamin Franklin introduced the idea that all substances
are penetrated with what he called electrical fluid or electric fire. He stated that if you get too much
find more resources at oneclass.com
find more resources at oneclass.com
5
Figure 2.1: Electrons are in a cloud around the nucleus. The nucleus is consist
of protons, which are positive charged, and neutrons, which have no net electric
charge. So the nucleus is positive. Electrons are negative charged.
of the fire, you would get positively charged and if you have a deficiency, you would get negatively
charged. Hence, he introduced the sign convention which is still in use.
If a positive charge is created in a medium by removing its electrons,then the electrons should
have moved to another medium. Therefore, the second medium becomes negatively charged.Hence,
you cannot create any charge. You can only ”distribute” it!
The following observations could be done from Franklin’s experiments:
1.
Same charges repel while opposites attract. So ”+” and ”+” or ”-” and ”-” repel; ”+” and ”-
” attract.
2.
More the charges, the more the force.
3.
Closer the charged objects, higher the force.
4.
Some materials ”conduct” the charges and others do not. Thus there are conductors and
insulators. Conductors are materials in which electrons are weakly bonded and can be stripped
off easily from the atoms.
In an experiment, lets take a glass rod and positively charge it and bring it close to a conducting
balloon (as shown in Fig. 2.2). In a conductive balloon, electrons are free to move around and they
will be attracted to the rod. This is called ”induction”.
Figure 2.2: Induction of poles using a glass rod.
10
−
8
cm
10
−
12
cm
⊕
elec
g
trons
electrons
g
Nucleus
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
At the heart of the topics are the four famous equations known as the maxwell"s equations, At the end of this course you will understand what each of these equations stand for. These equations would lead to the unification of electromagnetism with light and are responsible to explain many wonderful phenomena you see in daily life. Warning: this course is extremely math intensive and it would build upon the materials taught during the lectures. So you have to keep up or else you will be lost. Even sparing a week will put you in trouble. We would try to explain phenomena seen in life and connect them to electricity and magnetism. For example, lightening, magnetic levitation, northern lights, why is the sky blue, rainbows, etc. Our goal is to make you see through these equations, to make you see and understand the beauty around you and in doing so fell in love with physics.
