Download Physics 200 Class #1 Outline

Physics 200 Class #9 Notes
October 5, 2005
Reading Assignment for Monday
Chapter 5 pp. 106-140



from last time: Electric and Magnetic Fields
Continuation of Chapter 5 and Class #8 Notes
Reminder: The MidTerm Exam is on Monday, October 17th
A brief discussion of Energy: Appendix A (page 310)
Representing the Field: We represent the field by drawing arrows giving the direction and
strength (length) at each point in space surrounding a charge. It is not reasonable to draw too many
arrows since the picture would soon become too complicated. It is conventional to simply draw
one long arrow away from a positive charge. Keep in mind that the field gets stronger as we
approach the charge.
E points away from positive charges and towards negative charges.
Examples: See text
Magnetic Fields
It is easy to visualize the magnetic field lines around a bar magnet using iron filings.
Now the question is: How do we find the force on a charge?
Experiments show that the force on a stationary charge is zero and the force on a moving charge is:
F  qvb if v is perpendicu lar to B plus a direction given by the right hand rule!
F  qvB sin( angle between v and B)
Phy 200 Fall 2005 Class_9
Page 1 of 7
**************************************
Demonstration using cathode rays (electrons)
**************************************
More Examples:
Magnetic Field due to an electric current in a wire:
Phy 200 Fall 2005 Class_9
Page 2 of 7
Contributions of James Clerk Maxwell
Maxwell summarized all of the electricity and magnetism experiments and realized that it took
time for light to travel from one point to another. One of his major contributions led to our
knowledge of light as an electromagnetic phenomenon.
We now know:
c = 3 x 108 m/s
Energy and momentum can be transported by the fields themselves.
Maxwell’s Equations are the equivalent of Newton’s Laws of motion but for electromagnetic
forces ~ middle of the nineteenth century:
 E  dA 
Qenclosed
0
 B  dA  0
d
 E  dl   dt  B  dA
 B  dl   I   
0
0 0
d
E  dA
dt 
One result:
Notice the d/dt parts. That looks at the part that changes over time.
Changing electric fields produce changing magnetic fields and changing magnetic fields produce
changing electric fields.
Hertz demonstrated these EM waves for the first time with a spark gap transmitter and receiver.
The spark in the transmitter caused a spark in the receiver on the far side of the lab.
Phy 200 Fall 2005 Class_9
Page 3 of 7
The picture of Electromagnetic Waves then and now is:
Since electric fields and magnetic fields can exert force on stuff that has charge - electrons,
antennas, you and me - we should look at what force is. Also, if the fields can move things, then
energy is involved.
A brief discussion of Energy: Appendix A (page 310)
To this point, we have not discussed in any detail the energy carried by light waves. In the
late 19th century, we are close to the point in history where physicists attempted to explain in detail
the nature of spectra and the energy distribution in these spectra. We will review some energy (and
momentum) concepts by starting with Newtonian particles again.
Outline:
 A force acting through a given distance, independent of time (energy)
 A force acting for a given length of time, independent of distance
Energy
Force: A push or a pull
Mass: A measure of the inertia of an object. Can be defined in collision problems
Acceleration: Time rate of change of velocity
Phy 200 Fall 2005 Class_9
Page 4 of 7
Newton’s General Law F  ma provides a quick way to define the SI units for force:
m
 F   kg 2  newton
s
What does it take to generate a force?
How do we move things-what price do we pay?
Energy is the central unifying concept of physical science.
If we look at many cases of motion, we find that we need:
(a) a conservation law based on a non-directional measure of motion
(b) to describe the effects of a force when the direction relative to the motion changes
(c) the connection to heat
It is convenient to start with the concept of work.
Work is defined by the product of force and the distance through which the object moves under
the action of the force. Lift a box, you're exerting a force over a distance. You're changing the
potential energy of the box so you're doing work on the box. Work = change in potential energy.
Work = force x distance
Units: newton · meter
(where the force is acting in the direction of the motion)
We call this one joule
Time is not explicitly involved!
Power is the time rate of doing work or increasing (or using) the energy. The unit of
Power is joules/s = 1 watt.
[A short discussion of the purchase of energy is appropriate here. The energy can be
expressed as the product of power and time:
energy = power · time, so the unit is watt · second. A more convenient unit is the
kilowatt · hour (kWh) In terms of simpler energy units, the latter is
1000 watts x 3600 s = 3,600.000 = 3.6 x 106 joules.
My electric bill indicates that I pay about 8 cents per kWh for the first 400 kWh and
about 6.5 cents per kWh for the next 400 kWh.]
Energy is that which enables an object to do work. Or, if you prefer, energy is the ability to melt
ice. We have:
Potential Energy: A form of energy due to the relative position of interacting objects.
Kinetic Energy: A form of energy due to the motion of interacting objects.
And the total amount of energy doesn't change. Energy can take different forms - turn the calories
of that candy bar into fat (potential energy stored in the chemicals of your fat) or into kinetic
energy (run around the block instead).
Potential Energy (PE) (you could just write E but PE makes it more clear)
An object may store energy because of its position relative to some other object.
Phy 200 Fall 2005 Class_9
Page 5 of 7
An important example: Gravitational Potential Energy (equal to the work done against gravity in
raising an object)
gravitational Potential Energy = weight x height
PE = mgh
height is the distance above some reference level! Strictly speaking, mgh is the change in
gravitational PE over some height h. Not an absolute quantity. The potential energy of a book on a
table relative to the floor is a positive value, you gain kinetic energy if the book moves from the
table to the floor. The potential energy a person standing on the floor relative to a basket ball hoop
above them is a negative value. You have to add kinetic energy to get to the hoop.
electrical potential energy: potential energy due to the electric force. One way of defining energy
is Energy=Force x distance. Look at the force -
F k
q1 q 2
r2
.
Very very far away, r is very very big and F is about 0. At r = infinity, F=0. The energy a system
can gain by moving the charges away to infinity is the potential energy. It's like the energy a
gravitational system can gain in moving things from some shelves to the floor. In the case of
gravity, you always gain energy moving things down to the floor. With charges, you can have
different signs for the charges so the potential energy may be positive or negative.
So, using energy = force x distance for this example: the electrical potential energy (PE) is
qq
PE = F r
PE  k 1 2 , you only have one "r" on the bottom now for potential energy of an
r
electric field. When you work this out, remember the + and - signs of the charges. These change
the
electrical potential: Now we define a new quantity: "electrical potential" not "electrical potential
energy". This is a confusing name but don't be confused. The concept is simple. It's useful
quantity when working with electronics so that's why we cover it. We usually determine:
potential energy PE
joules

 volt
charge
Q
coulomb
Kinetic Energy (KE) (you could just write E but KE makes it more clear)
If an object is moving, it is capable of doing work
We can see the effect of this by looking at the case of constant force.
v
F  x  m a x  m final (vavet )  mv final ( 12 v final )  12 mv 2final
t
we see that the product of force and distance gives us a change in the quantity ½ m v2. We call this
latter quantity the kinetic energy (energy due to motion).
Work-Energy Theorem
Work = change in KE
Since energy is conserved, if you have a change in KE you have a change in PE so this is just a
restatement of: Work = change in PE.
Phy 200 Fall 2005 Class_9
Page 6 of 7
Conservation of Energy Principle
Energy cannot be created or destroyed; it may be transformed from one form to another, but the
total amount of energy never changes.
A more limited conservation law can be written for Mechanical Energy:
PE + KE = constant
Thermal and Radiant energy (see below) are more involved are still the same energy. Heat is just
molecules bouncing around - kinetic energy. Stored energy is just potential energy.
Thermal Energy: We define the energy required to heat I kilogram of water one Celsius degree to
be one Calorie. (the “mechanical equivalent is 4186 joules)
(strange notation alert: 1 Capital C Calorie is equal to 1000 lowercase c calories. 1 cal = 4.186 J
and 1 Cal = 4186 J. Food Calories are upper case C, you're getting alot of energy from that candy
bar! See http://www.bartleby.com/64/C004/012.html )
Radiant Energy: The energy carried by electromagnetic waves. Maxwell showed that the radiant
energy carried by an electromagnetic wave is proportional to the electric field squared:
Radiant Energy  E 2
Key Point of radiant energy: In classical physics the energy of a system can take on a continuous
set of values!
We'll talk about how energy and momentum are related next time. For examples, look at
http://www.kungfuscience.org
Phy 200 Fall 2005 Class_9
Page 7 of 7