Transcript lecture01
Welcome… …to Physics 2135.
PHYSICS 2135 (previously 24) Engineering Physics II Spring 2015 Dr. Allan Pringle Course Instructor Room 122 Physics, 341-4031 http://www.mst.edu/~pringle [email protected]
Lectures: http://physics.mst.edu/classes/class24/ Online quizzes: blackboard.mst.edu
Announcements
In recitation yesterday, you picked up the handout containing: Course Handbook Syllabus (course schedule and assigned homework) Starting Equations Special Homework assignments .
Make sure you recorded your recitation instructor’s name and your recitation section letter on the first page of the handout.
Under the new course numbering scheme, Physics 24 has become Physics 2135. You will need to look for Physics 2135 when you log in to Blackboard. Engineering Physics I is now Physics 1135. I will frequently refer to that course as Physics 23, because that’s what it was for many decades!
From the syllabus:
read 1: 1-4
recitation number 2
2. Thursday, January 22
1: 13, 18 (also express the force in unit vector
notation), 28, 87, Special Homework #1 chapter 1 You can find homework assignments online here: http://campus.mst.edu/physics/courses/24/Assignments/syllabus.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 7:30-9:30 AM on Friday, May 15, 2015.
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 not receive a lab grade (15% of the course points) if you don’t have a lab manual!
Our text is a custom edition of
University Physics with Modern Physics
, Young and Freedman, 13 th 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
Mastering Physics is included in the package you buy at the bookstore.
You may use Mastering Physics as a supplement to lectures and recitations.
I will “assign” all of the Mastering Physics material that is related to Physics 2135. This is optional material, and will not *count towards your course grade.
Instructions for signing up for Mastering Physics are here .
*Knowledge you acquire while using Mastering Physics could improve your course grade.
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 1.1 and 1.2 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 1.1 and 1.2.
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 q 1 and q 2 (in units of Coulombs), where r 12 is the distance in meters between the charges, and k=9x10 9 N ·m 2 /C 2 .
F 12
k q q
1 2 2
r
12 *Moving charged particles also exert the Coulomb force on each other.
a note on starting equations
F 12
k q q
1 2 2
r
12 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.
F E
k Q Q D
2 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.
F 12
k q q
1 2 2
r
12 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 all components).
Also,
k
1 4
0
where
0 12
C
2 2
.
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, r 12 distance between the centers of the spheres.
is the r 12 + I just told you it’s OK to use Coulomb’s Law for spherically-symmetric charge distributions.
If more than one charge is 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 Q 1 = +Q is located a distance d along the y-axis from the origin. A second positive charge Q 2 = +Q is located at the origin and a negative charge Q 3 = -2Q is located on the x-axis a distance 2d away from Q 1 . Calculate the net electrostatic force on Q 1 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.
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 I will do in lecture.
Or you may write F x 3 kQ 2 4 d 2 F y 3 kQ 2 4 d 2 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 F 2 Q 1 =+Q d
F
F 3 2d Q 2 =+Q Q 3 =-2Q x If Q 1 were free to move, what direction would its initial acceleration be? How would I calculate the acceleration?
Would the acceleration remain constant as Q 1 moved? Could I use the equations of kinematics (remember them from Physics 1135?) to describe the motion of Q 1 ?
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.
F = 12 1 4πε
0
q q
1
r
2 12 2
,
+ Q 1 r 12 Q 2 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
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.
+ F 12 F 13 like charges repel + F 21 F 31 unlike charges attract A charged particle modifies the properties of the space around it.
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.” + F 12 F 13 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!
Trust me. Or go stand outside in an electric storm and then try to tell me the electric field is not real.
+ F 21 like charges repel F 31 unlike charges attract 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 q 0 :
F E = q
0 0 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
F E = lim
q 0 0
q
0 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.
0 0
= N C
In chapter 3, you will learn that the units of electric field can also be expressed as volts/meter:
N = C V 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.
F =G
G
m m
1 2 2
r
12
, attractive g(r) = F
G
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
F =k 12 q q
1 2 2
r
12
,
... which tells us the electric field due to a point charge q is
q E =k
q
r
2
, away from +
…or just…
E=k q r
2 This is your third starting equation.
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.
point… ˆr source point ˆr + field point …then the equation for the electric field of a point charge becomes:
E=k r q ˆ r
2
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 + D -eP E P E P k q r 2 k(+e) D 2 9 11 2 19 E P 11 N C For comparison, air begins to break down and conduct electricity at about 30 kV/cm, or 3x10 6 V/m.
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 +q + -q d
+q + P E L d -q
E
qd 4
o
r
3 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 v 0 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 v 0 E + + + + + + + + + + + + + To be worked at the blackboard in lecture.
What would be different for a proton?
v fx x f v ix a x t x i v ix 1 2 a x 2 Make sure you understand what a uniform electric field is.
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.
q E=k r 2 Make sure you understand which kind of problem you are working on!
Homework Hints (may not apply every semester) Symmetry is your friend. Use it when appropriate. Don’t use it when not appropriate.
F
G,pair
GmM , attractive r
2 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:
F 12
k q q
1 2
r
12 2
F E = q
0 0 (plus Physics 1135 starting equations).
E=k q r
2 Remove the absolute value signs
ONLY IF
charges are positive.
you know that all E = F q q = 0 0 F E