Welcome…
…to Physics 2135.
PHYSICS 2135
Engineering Physics II
Spring 2016
Dr. Allan Pringle
Course Instructor
Room 122 Physics, 341-4031
http://www.mst.edu/~pringle
pringle@mst.edu
Lectures:
http://physics.mst.edu/classes/class24/
Online quizzes: blackboard.mst.edu
Announcements
Make sure you pick up the handout containing:
Course Handbook
Syllabus (course schedule and assigned homework)
Starting Equations
Special Homework assignments.
If you are in the online lecture section, you can pick this
handbook up during your first recitation.
For those of you who don’t have the course handbook yet, the
homework assignment for tomorrow is on the next slide.
Make sure you record your recitation instructor’s name and
your recitation section letter on the first page of the handout.
From the syllabus:
read 21: 1-4
Read
this!
recitation
number 1
2. Thursday, January 21
21: 14, 26, 36, 74, Special Homework #1
chapter 21
You can find homework assignments online here:
http://campus.mst.edu/physics/courses/24/Assignments/syllabus.pdf
“Official Starting Equations” are available here:
http://campus.mst.edu/physics/courses/24/Handouts/ose.pdf
Your recitation instructor will call students to the board
tomorrow to present their homework solutions to the class.
If you are called on to do boardwork, you may use your
calculator, a blank handout problem sheet (which we will
provide), and the starting equation sheet. Nothing else. We do
understand that this is the first week of class.
Homework help will be available in the Physics Learning
Center (PLC), rooms 129 and 130 Physics, from 2-4:30 pm and
6-8:30 pm.
The Physics 2135 Final Exam will be from 3:00-5:00 PM on
Wednesday, May 11, 2016. Make sure you have nothing else
scheduled during this time period!
Go to http://physics.mst.edu/currentcourses/labs/index.html to get a lab
schedule. There are no labs this week. Odd-numbered
sections meet next week (3L05 is odd, 3L06 is even).
You must purchase a lab manual. Go to the department
office, room 102, to purchase your lab manual! The cost is
$25.00. Do not ask me for a lab manual; I do not have
them!
You will receive a lab grade of zero (and lose 15% of the
possible course points) if you don’t have a lab manual!
Our text is University Physics with Modern Physics Vol. 2,
Young and Freedman, 14th Edition
Full Text
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Chapter 25
Chapter 26
Chapter 27
Chapter 28
Chapter 29
Chapter 32
Chapter 33
Chapter 34
Chapter 35
Chapter 36
Custom Text
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
For several semesters prior to
this, we used a custom edition of
the text (13th edition). You may
use that text. Here is a table
showing the correspondence
between chapter numbers in Vol.
14 and the custom edition.
If you use the 13th edition or the
custom text, you must follow the
instructions here; otherwise you
will not work the correct
homework problems!
This semester we study electromagnetic forces and their
consequences.
These forces are responsible for holding together living
and man-made things, as well as all things in nature, so I
suppose they are worth studying…
…not to mention the fact that the technology that
dominates your life depends on electromagnetic forces.
Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
Electric Charge
Read about electric charge in sections 21.1 and 21.2 in your
text. You should have learned this material in your prior
academic career. If you haven’t, there is important information
you need to learn now!
There are two kinds of charge.
+
-
 like charges repel
 unlike charges attract
 charges can move but charge is conserved
Law of conservation of charge: the net amount of electric
charge produced in any process is zero. (Not on your starting equation
sheet, but a fact that you can use any time.)
Although there are two kinds of charged particles in an atom,
electrons are the charges that usually move around.
+
-
A proton is roughly 2000 times more massive than an
electron and are typically bound inside nuclei.
Charges are quantized (come in units of e= 1.6x10-19 C).
The charge of an electron is –e = –1.6x10-19 coulombs.
The charge of a proton is +e = +1.6x10-19 coulombs.
That’s all the lecture time I’ll devote to sections 21.1 and 21.2.
Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged
particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
Coulomb’s Law
Coulomb’s law quantifies the magnitude of the electrostatic*
force.
Coulomb’s law gives the force (in newtons) between charges q1
and q2 (in units of coulombs), where r12 is the distance in meters
between the charges, and k=9x109 N·m2/C2.
q1q 2
F k 2
12
r12
*Moving charged particles also exert the Coulomb force on each other.
a note on starting equations
q1q 2
F k 2
12
r12
is on your starting equation sheet.
In general, you need to begin* solutions with starting equations.
You may begin with any correct variant of a starting equation.
For example, F  k
E
QA QB
D
2
is “legal” and may be used.
Don’t get hung up about starting a problem with an equation
which is an exact copy of one from the OSE sheet.
*“Begin” does not mean that a starting equation has to be the first thing that appears
on your paper. It might be several lines before you use a starting equation.
Force is a vector quantity. Your starting
equation gives the magnitude of the force.
Use your diagram for the problem to figure
out the direction. If the charges are opposite
in sign, the force is attractive; if the charges
are the same in sign, the force is repulsive.
q1q 2
F k 2
12
r12
This equation just gives the
magnitude of the force.
I want this class to make you
hear little voices in your head.
If a problem asks you to calculate a force, assume that means
both magnitude and direction (or else all components).
1
Also, k 
40
where
0  8.85 1012
C2
.
2
Nm
Remember, a vector has a magnitude and a direction.
Coulomb’s Law is valid for point charges. If the charged objects
are spherical and the charge is uniformly distributed, r12 is the
distance between the centers of the spheres.
r12
-
+
I just told you it’s OK to
use Coulomb’s Law for
spherically-symmetric
charge distributions.
If more than two charges are involved, the net force is the vector
sum of all forces (superposition). For objects with complex
shapes, you must add up all the forces acting on each separate
charge (calculus!!).
+
+
+
-
-
-
Example: a positive charge Q1 = +Q is located a distance d
along the y-axis from the origin. A second positive charge
Q2 = +Q is located at the origin and a negative charge Q3 = -2Q
is located on the x-axis a distance 2d away from Q1. Calculate
the net electrostatic force on Q1 due to the other two charges.
To be worked at the blackboard. You should apply the expert
techniques you learned in Physics 1135 when you work
Physics 2135 problems.
Skip to slide 21.
Example: a positive charge Q1 = +Q is located a distance d
along the y-axis from the origin. A second positive charge
Q2 = +Q is located at the origin and a negative charge Q3 = -2Q
is located on the x-axis a distance 2d away from Q1. Calculate
the net electrostatic force on Q1 due to the other two charges.
y
Q1=+Q
d
Q2=+Q
2d
Q3=-2Q
x
Calculate the net electrostatic force on Q1 due to the other two
charges.
F  F2  F3
y
 +Q  +Q  ˆ Q2 ˆ
q1q2 ˆ
F2  k 2 j  k
j k 2 j
2
r12
d
d
F2
Q1=+Q

F3
d
F3  F3x ˆi  F3y ˆj
F3  F3 cos ˆi  F3 sin ˆj
2d

Q2=+Q
Q3=-2Q
F12 = k
sin  
x
q1q2
r122
1
2
cos 
3
2
Note: F2 and F3 are not drawn to scale (F3 is “too long”).
q1q3
q1q3
ˆ
F3  k 2 cos i  k 2 sin ˆj
r13
r13
 +Q  -2Q 
F3  k
2
2d
 
 +Q  -2Q  1 ˆ
3ˆ
i  k
j
2
2
2
 2d
Calculate the net electrostatic force on Q1 due to the other two
charges.
 +Q  -2Q 
F3  k
2
 2d
y
F2
Q1=+Q
2Q2 3 ˆ
2Q 2 1 ˆ
F3  k
i  k
j
2
2
4d 2
4d 2

F3
d
 +Q  -2Q  1 ˆ
3ˆ
i  k
j
2
2
2
 2d
3 kQ 2 ˆ 1 kQ 2 ˆ
F3 
i 
j
2
2
4 d
4 d
2d

Q2=+Q
Q3=-2Q
F12 = k
x
q1q2
r122
1
sin  
2
3
cos 
2
Note: F2 and F3 are not drawn to scale (F3 is “too long”).
Q2 ˆ
3 kQ 2 ˆ 1 kQ 2 ˆ
F  F2  F3  k 2 j +
i 
j
2
2
d
4 d
4 d
3 kQ 2 ˆ 3 kQ 2 ˆ
F
i 
j
2
2
4 d
4 d
Comments:
Once you have become an expert at problems like this, you can
combine and perhaps even skip some steps.
Skipping steps on work to be graded is not recommended!
You may express your answer in unit vector notation, as on the
previous slide.
Or you may write
3 kQ 2
Fx 

2
4 d
3 kQ 2
Fy 

2
4 d
You may also express your answer as a magnitude and
direction.
All three of the above ways of writing F completely specify the
vector.
y
F2
Q1=+Q
d
Q2=+Q
F

F3
2d

Q3=-2Q
x
If Q1 were free to move, what direction would its initial
acceleration be? How would I calculate the acceleration?
Would the acceleration remain constant as Q1 moved? Could I
use the equations of kinematics (remember them from Physics
1135?) to describe the motion of Q1?
Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
Coulomb’s Law:
it’s just part of a bigger picture
Coulomb's Law quantifies the interaction between charged
particles.
1 q1q 2
F =
,
2
12 4πε 0 r12
r12
+
-
Q1
Q2
Charged particles exert forces on each other over great
distances.
How does a charged particle "know" another one is “there?”
We use the concept of an electric field to explain this
interaction. Here's the idea…
The Electric Field
F12
 A charged particle propagates (sends
out) a "field" into all space.
 Other charged particles
sense the field, and “know”
that the first one is there.
+
+
like
charges
repel
A charged particle modifies the
properties of the space around it.
F21
F13
F31
unlike
charges
attract
The idea of an electric field is good for a number of reasons:
 It makes us feel good, like we’ve
actually explained something.
OK, that was a flippant remark. There are serious reasons
why the idea is “good.”
 We can develop a theory based on this
idea. From this theory may spring
unimagined inventions.
If the theory explains past observations and leads to new
predictions, the idea was “good.”
 The electric field is real!
F12
+
F13
F31
+
F21
like
charges
repel
unlike
charges
attract
Trust me. Or go stand outside in an electric storm and then
try to tell me the electric field is not real.
Some physicists will tell you the electric field is real. Others disagree. It seems to depend on what you define “real” to mean.
We define the electric field by the force it exerts on a test
charge q0:
F0
E=
q0
The subscript “0” reminds you the force is on the
“test charge.” I won’t require the subscripts when
you use this equation for boardwork or on exams.
If the test charge is "too big" it perturbs the electric field, so the
“correct” definition is
F0
E = lim
q 0 0 q
0
You won’t be required to use
this version of the equation.
Any time you know the electric field, you can use this equation to calculate the force
on a charged particle in that electric field: F = qE
This version of the electric field equation is on your equation
sheet. Use it for problems involving electric fields and forces:
I’m not mad, I tell you, not mad. The
little voices tell me I’m quite sane.
F = qE
This is your second starting equation. The equation tells you the direction of the
electric field is the direction of the force exerted on a POSITIVE test charge. The
absence of absolute value signs around q means you MUST include the sign of q in
your work.
The units of electric field are
newtons/coulomb.
 F0  N
 E  =   =
q0  C
In chapter 23, you will learn that the units of electric field can
also be expressed as volts/meter:
N V
E = =
C m
The electric field can exist independent of whether there is a
charged particle around to “feel” it.
Remember: the electric field direction is the
direction a + charge would feel a force.
+
A + charge would be repelled by another + charge.
Therefore the direction of the electric field is away from
positive (and towards negative).
http://regentsprep.org/Regents/physics/phys03/afieldint/default.htm
Gravitational Fields
The idea of a field is not new to you. You experienced fields
(gravitational) in Physics 1135.
m1m 2
FG =G 2 , attractive
r12
FG
g(r) =
m
Units of g are
actually N/kg!
g(r) is the local gravitational field. On earth, it is about 9.8
N/kg, directed towards the center of the earth.
A particle with mass modifies the properties of the space around it.
If the last equation
looks like this, you
have missing fonts.
Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
The Electric Field
Due to a Point Charge
Coulomb's law says
q1q 2
F =k 2 ,
12
r12
... which tells us the electric field due to a point charge q is
E q =k
q
r
2
, away from +
…or just…
This is your third starting equation.
q
E=k 2
r
q
E=k 2
r
A physics 2135 equation is like a toaster!
You wouldn’t shove
yogurt down your
toaster, would you?
You can’t expect to just shove numbers into an equation and
out pops the correct answer.
To experience the optimum user satisfaction from your physics
2135 toaster equations you need to understand what they
mean and think about what you are doing with them.
If we define r̂ as a unit vector from the source point to the field
point…
source point
r̂ +
field point
…then the equation for the electric field of a point charge
becomes:
q
E=k 2 rˆ
r
Consult a professional before using. Do not use more
than 4 times a day without seeing your physicist.
May cause headaches, dizziness, and upset stomach.
Drink a full glass of water with each use.
You may start with either equation
for the electric field (this one or the
one on the previous slide). But
don’t use this one unless you
REALLY know what you are
doing! (So for now don’t use it!)
Example: calculate the electric field at the electron’s distance
away from the proton in a hydrogen atom (5.3x10-11 m).
+e
+
-e
P
-
EP
k q k(+e)
EP  2 

2
r
D
D
E P  5.110
11
9 109 1.6 1019 
 5.3 10 
N
C
For comparison, air begins to break down and conduct
electricity at about 30 kV/cm, or 3x106 V/m.
11 2
A Dipole
A combination of two electric charges with equal magnitude and
opposite sign, separated by a fixed distance, is called a dipole.
- -q
+q +
d
The charge on this dipole is q (not zero, not +q, not –q, not
2q). The distance between the charges is d. Dipoles are
“everywhere” in nature.
This is an electric dipole. Later in the course we’ll study magnetic dipoles.
The Electric Field of a Dipole
Example: calculate the electric field at point P, which lies on the
perpendicular bisector a distance L from a dipole of charge q.
P
to be worked at the
blackboard in lecture
L
Skip to slide 41.
- -q
+q +
d
Example: calculate the electric field at point P, which lies on the
perpendicular bisector a distance L from a dipole of charge q.
y
E+


P
r
+q +
E = E  E
L

E y = 0 (symmetry)
E x = 2E  ,x (symmetry)
Er
E x = +2E  cos 

d
- -q
x
Example: calculate the electric field at point P, which lies on the
perpendicular bisector a distance L from a dipole of charge q.
y


P
r
+q +
E x = +2E  cos 
E+
L
 d/2
d/2
d
E x = +2E 
= +E 
r
r
Er
d/2  -q
d
Ex
x
k q d
kqd
=+ 2
= 3
r r
r
qd ˆ
E =
i
3
4 0 r
“Charge on dipole” is positive by
convention, so no absolute value
signs needed around q.
P
E
qd
E
4 o r 3
L
- -q
+q +
d
Caution! The above
equation for E applies
only to points along
the perpendicular
bisector of the dipole.
It is not a starting
equation.
(r is not a system parameter, but let’s
not worry about that right now)
Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric
field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
Motion of a Charged Particle
in a Uniform Electric Field
A charged particle in an electric field experiences a force, and if
it is free to move, an acceleration.
If the only force is due to the
electric field, then
 F  ma  qE.
- - - - - - - - - - - - -
-
F
E
+ + + + + + + + + + + + +
If E is constant, then a is constant, and you can use the
equations of kinematics* (remember way back to the beginning
of Physics 1135?).
*If you get called to the board, you can use the Physics 1135 starting equations. They are posted.
Example: an electron moving with velocity v0 in the positive x
direction enters a region of uniform electric field that makes a
right angle with the electron’s initial velocity. Express the
position and velocity of the electron as a function of time.
y
- - - - - - - - - - - - -
x
-e
E
v0
+ + + + + + + + + + + + +
Skip to slide 48.
To be worked at the blackboard in lecture.
What would be different for a proton?
vfx  vix  a x t
1
2
x f  x i  vix t  a x  t 
2
Make sure you understand what a uniform electric field is.
Express the position and velocity of the electron as a function of
time.
FE = qE =  -e  E = -eEjˆ = ma
y
-e
v0
FE a
E
x
eE ˆ
a=j
m
ax = 0
eE
ay = m
Let’s work the rest of the problem one component at a time.
Express the position and velocity of the electron as a function of
time.
eE
ay = m
ax = 0
y
0
-e
v0
FE a
E
x
1 2
x = x i + vix t + a x t
2
x = v0 t
0
0
1 2
y = yi + viy t + a y t
2
Position:
x = v0 t
0
1 eE 2
y=t
2 m
y=
1 2 1 eE 2
a yt = t
2
2 m
Express the position and velocity of the electron as a function of
time.
eE
ay = m
ax = 0
y
0
-e
v0
FE a
E
x
vx = vix + a x t
v x = v0
0
v y = viy + a y t
Velocity:
v x = v0
eE
vy = - t
m
v y = a y t= -
eE
t
m
What is the shape of the electron’s path?
y
-e
x = v0 t
v0
FE a
E
x
t=
y=-
1 eE 2
t
2 m
x
v0
2
 1 eE  2
1 eE  x 
y=x
  = -
2 
2 m  v0 
 2 mv 0 
The trajectory of the electron is a parabola, concave down.
Just like the trajectory of a ball thrown horizontally in the
gravitational field of the Earth.
Concluding Remarks
Homework Hints (may not apply every semester)
There are two kinds of electric field problems in
today’s lecture:
1. Given an electric field, calculate the force on a
charged particle.
F = qE
2. Given one or more charged particles, calculate
the electric field they produce.
E=k
Make sure you understand which kind of problem you are
working on!
q
r2
Homework Hints (may not apply every semester)
Symmetry is your friend. Use it when appropriate. Don’t use it
when not appropriate.
FG,pair
GmM

, attractive
2
r
The above equation is on the Physics 1135 Starting Equation
Sheet, which is posted in the recitation classrooms. You are free
to use Physics 1135 starting equations at any time.
Homework Hints (may not apply every semester)
Your starting equations so far are:
q1q 2
F k 2
12
r12
F0
E=
q0
q
E=k 2
r
(plus Physics 1135 starting equations).
Remove the absolute value signs ONLY IF you know that all
charges are positive.
F0
F0
NEVER do this: E =
(why?)
 q0 =
q0
E
Learning Center Today
2:00-4:30, 6:00-8:30
Rooms 129/130 Physics