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Problem 1
In the figure below, a central particle of charge is surrounded by two circular rings of
charged particles. What are the magnitude and direction of the net electrostatic force on
the central particle due to the other particles ?
a) 0

A rod made of two different materials
plastic
L
2
gold
L
2
A rod made of two different materials
plastic
L
2
gold
L
2
A rod made of two different materials
plastic
L
2
gold
L
2
rod made of four materials
paper
silver
gold
plastic
L
4
L
4
L
4
L
4
All are d

Chapter 23
Search the web for information on the following topics
Electric forces in DNA: base pairing
Electrophoresis
How do Sharks sense electric fields?
Inkjet printers

Chapter 23
LCD screens:
The concept in Electricity that this technology uses:
If a charge is placed in an electric field, it experiences a force.
How the technology works:
http:/www.youtube.com/watch?v=O3aITfU_UvE
http:/www.youtube.com/watch?v=uh9SqvBVRwk

Chapter 23
Dielectric heating:
The concept in Electricity that this technology uses:
If a charge is placed in an electric field, it experiences a force.
How the technology works:
http:/phet.colorado.edu/en/simulation/microwaves
Permanent Dipole molecules

Charge 1 makes a force on charge q
Charge 2 makes a force on charge q
Charge 3 makes a force on charge q
The total force on charge q is the vector sum of
all the forces of each charge on q
We can separate the problem into two parts by taking the charge q

Chapter 23
E ink:
The concept in Electricity that this technology uses:
If a charge is placed in an electric field, it experiences a force.
Resources: http:/www.eink.com/
How the technology works:
http:/www.eink.com/technology.html
http:/www.youtube.com/w

Motion of charged particles in a uniform electric field
Nice animation for motion of charges in a field
http:/phet.colorado.edu/en/simulation/electric-hockey

There is a common misconception that taking the limit of a sum when the
variable goes to zero will be problematic
So the limit exists and there is no problem evaluating it
The Fundamental theorem of calculus
For the problem we just solved
The Fundamental

There is a common misconception with the definition of a derivative that
dividing by delta x and taking the limit when delta x goes to zero would be
problematic
It is clear that when we follow the procedure through we have no problem in the end

What is the electric field at point p ?
Step 1: identify an
element of charge
somewhere on the line
Step 2: get the electric
field due to this element
at point p. this is the
electric field of a point
charge
Step 3: write the
element of charge in
terms of

Constant linear mass denisty
L
Rod of negligible thickness of length L
And total mass M
The mass per unit length of the rod is
The total mass of the rod is
Cut the rod in two equal halves
L
2
mass per unit length of
the left rod
mass per unit length of
th

Scalar field
At every point in space there is a number associated with each point
Example: temperature field. At each point we can measure the
temperature which is a number
Vector field
At every point in space there is a vector associated with each point

Strength of Materials
ENGR 2112
1
Motivation
Studying How Engineering Materials Fail?
CONTROL
AVOID
2
Why & How
Engineering Materials Fail?
How will failure start/evolve?
Always where the load is applied? No!
Nature of material loaded
Nature of Load Appli