Download Exam 1 S15 Phys 1220

Exam 1 S15
Phys 1220
3/5/15
__________
name
Each problem is of equal value.
You can skip three of the seven problems. You must work at least one of problem
two and three, and one of problems four and five, and one of problems one and
six.
If you work more than the required problems, we will count the best four grades
in agreement with the above rules.
Tips for better exam grades:
Read all problems right away and ask questions as early as possible.
Make sure that you give at least a basic relevant equation or figure for each
problem part.
Make use of the entire exam time.
Show your work for full credit. The answer ‘42’ only earns you any credit IF
‘42’ is the right answer. We reserve points for ‘steps in between’, figures,
units, etc.
No credit given for illegible handwriting or flawed logic in your reasoning.
1. Lecture Video Discussion and Basic Lab Knowledge
Recall the lecture video on demonstrating the changing gap in plate
capacitors.
a) Describe the experimental setup that would demonstrate the physical
effects of changing the gap.
Hint: make sure to explain how the electroscope readings work.
b) Explain how the capacitance, charge, and potential difference across the
plates change when you double the gap.
c) Name one likely systematic experimental error and one likely random error
that might skew the results of such an experiment, assuming that great
care was taken to set the experiment up properly.
d) Explain how you would perform independent repetitions and explain what
would happen to the statistical data, if you did not do a good job at making
repetitions independent.
2. Electrostatics
A non-uniform, but spherically symmetric, distribution of charge has a charge density (r)
given as follows:
4∙𝑟
𝜌(𝑟) = 𝜌0 ∙ (1 − 3∙𝑅) 𝑓𝑜𝑟 𝑟 ≤ 𝑅 𝑎𝑛𝑑
𝜌(𝑟) = 0
𝑓𝑜𝑟 𝑟 > 𝑅
Where 0 is a positive constant.
a) Find the total charge contained in the charge distribution
b) Explain your choice of Gaussian surface you are going to use for part c) and explain why
and where the electric field is going to be uniform in that surface.
c) Using Gauss’s Law, obtain expressions for the electric field in both regions.
Hint: Show your steps for full credit.
d) Draw the E(r) graph from r= 0 to r= 2R. If you cannot solve part c) you can still draw the
graph qualitatively for partial credit.
Hint: Include in your drawing qualitative expressions for the steepness of the curves in
terms of Q, 0, and R and include exact E values on the vertical axis.
3. Electrostatics
Negative electric charge - 4Q is located on a conducting spherical shell of inner
radius 4a and outer radius 6a. Concentric within the first shell is a second
conducting shell that carries +6Q. Its inner radius is 1.5a and its outer radius is
2a.
a) Draw E(r) between r=0 and r=8a.
b) Draw V(r) between r =0 and r =8a.
Hint: Divide the problem into appropriate regions of r. Draw the graphs
quantitatively exact – this requires appropriate numbers on the axes. Label
the functional dependence, which each curve follows.
4. Electrostatics
Consider the following arrangement of point charges:
a) Determine the net field at P due to all four point charges. Show a vector
diagram for the field vectors due to each charge at P.
b) What is the potential energy required to bring these charges together? Take U=
0 at infinity.
5. Electrostatics:
Three point charges with charge -2q, +4q, and -2q are arranged along the x-axis
as shown (see figure). Are there points of zero potential along the x-axis?
Where are they? If there are none explain how you know this.
6. Capacitors
Consider the capacitor network shown below.
All capacitances are in micro-Farad.
a) Derive the equations for series and for parallel networks of capacitors.
b) What is the equivalent capacitance of the network in the figure?
c) If Vab = 110[V], how much energy is in the 3[F] capacitor?
7. Electrostatics
Which of the following statements are true, which are false? Mark clearly whether you consider a
statement true or false. Explain in the space below each question briefly why a statement is correct or
false.
A- A negative point charge causes everywhere in space an electric field that points inward toward the
point charge and the field is the stronger, the closer one gets to the point charge.
B- A negative point charge causes everywhere in space a negative potential. Approaching the point
charge lowers a charges potential energy.
C- Gaussian surfaces must have the same geometry as the object they are testing.
D- When an object possesses a non-uniform charge density then the total charge on the object is always
different from zero.
Master Equations – Physics 1220
𝐹=
1
4𝜋𝜀0
∙
|𝑞1 |∙|𝑞2 |
𝑟2
1
4𝜋𝜀0
𝐶 ≡
𝑄
𝑉𝑎𝑏
𝑈=
𝑄2
2𝐶
∑i
=
qi 𝑞0
ri
and V =
𝐶 𝑉2 =
𝑞0

𝜀0
𝑎𝑛𝑑 𝐶𝑝𝑙𝑎𝑡𝑒 = 𝜀0
1
2
𝐹0
𝑄𝑒𝑛𝑐𝑙.
 Φ𝐸 = ∫ 𝐸⃗ ∙ 𝑑𝐴 =
𝑈=
𝑎𝑛𝑑 𝐸⃗ =
1
2
𝐴
𝑑
U
q0
𝑎𝑛𝑑 𝐸⃗ = − (𝑖̂
𝑎𝑛𝑑, 𝑖𝑛 𝑠𝑒𝑟𝑖𝑒𝑠,
𝑄 𝑉 𝑎𝑛𝑑 𝑢 =
1
2
𝜕𝑉
𝜕𝑥
1
𝐶𝑒𝑞
𝜀 𝐸2
Also, from mechanics:
W = U = K, E = K + U = ½ m v2 + Uel.st.
1
𝐶2
9
= 9 ∙ 10 [
]
4𝜋𝜀0
𝑁 ∙ 𝑚2
+ 𝑗̂
𝜕𝑉
𝜕𝑦
1
+ 𝑘̂
𝜕𝑉
)
𝜕𝑧
= ∑𝑖 𝐶 , 𝑎𝑛𝑑, 𝑖𝑛 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙, 𝐶𝑒𝑞 = ∑𝑖 𝐶𝑖
𝑖
Need to take your mind of the exam for a second? Check this out:
Electric bulbs don't emit light; they suck dark. Thus they now call these bulbs dark suckers:
The basis of the dark sucker theory is that electric bulbs suck dark. Take for example the dark suckers in
the room where you are. There is less dark right next to them than there is elsewhere. The larger the
dark sucker, the greater its capacity to suck dark. Dark suckers in a parking lot have a much greater
capacity than the ones in this room.
Dark has mass. When dark goes into a dark sucker, friction from this mass generates heat. Thus it is not wise to
touch an operating dark sucker. Candles present a special problem, as the dark must travel in the solid wick instead
of through glass. This generates a great amount of heat. Thus it can be very dangerous to touch an operating candle.
Dark is also heavier than light. If you swim deeper and deeper, you notice it gets darker and darker. When you reach
a depth of approximately fifty feet, you are in total darkness. This is because the heavier dark sinks to the bottom of
the lake and the ligher light floats to the top.
Finally, we must prove that dark is faster than light. If you stand in an illuminated room in front of a
closed, dark closet, then slowly open the door, you would see the light slowly enter the closet, but since
the dark is so fast, you would not be able to see the dark leave the closet.
When Mr. Leno of the Tonight Show went J-walking and asked pedestrians some science
questions, he discovered some amazing new facts about the universe:
Jay Leno: "Why does dew appear on plants in the morning when the Sun comes up?" A
waitress: "Is it because the Sun makes them perspire?"
Jay Leno: "Why does the Moon orbit the Earth?" An auto mechanic: "To get to the other
side?"
Jay Leno: What are magnets?" A taxi driver: "Are they the things crawling over a weekold dead cat?"
Jay Leno: Which is more useful, the Sun or the Moon?" A thirteen-year old: [Pause] "I
think it's the Moon because the moon shines at night when you want the light, whereas the
Sun shines during the day when you don't need it."