Download Final Exam - Physics and Physical Oceanography

Physics 1051
Final Exam - Spring 2010
MUN Physics and Physical Oceanography
Name:
th
Friday, August 13 , 2010
Professor:
Student Number:
Rules
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Notes, text books and other aids besides a calculator are not permitted.
Examination time is 120 minutes. You must to stop writing when the time has elapsed.
Cellphones and electronic devices are not permitted.
You must answer ALL questions.
All necessary workings and details are required.
You are not to remove this page.
This paper has 11 pages including this one.
There are 10 multiple choice (20 marks total) and 8 long answer questions (10 marks each).
If something is not clear, you are allowed ask for clarification!
Good luck and do what you can.
Formulae
Maxwell's Equations
Constants
Mathematical Formula
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Multiple Choice [2 marks each, 20 marks total]
Circle the correct response.
1. Let's say you are doing a physics 1051 lab in C-2039. If the lab was about a simple pendulum, you
would likely discover that it's period depends on
a. on amplitude of the motion only.
b. only on the length of the string.
c. only on the acceleration due to gravity.
d. both b and c.
2. Given that electric field and magnetic field are similar but different, pick the following statement
that is NOT true regarding them.
a. Magnetic field can be created from both a stationary charge and a moving charge
b. Electric field can be created from both a stationary charge and a moving one.
c. Electric field can do work and magnetic field cannot.
d. A repulsive force occurs of the electric type between two charges of like charge and of the
magnetic type for parallel wires of current in opposite directions.
3. Displacement current (different from conduction current) appears in Maxwell's equations. Select
the statement that describes where it occurs.
a. First term in R.H.S. of
b. Second term in R.H.S. of
c. Term in R.H.S. of
d. Term in L.H.S. of
4. Which on of the following is NOT true of electric field lines.
a. The number of field lines that touch a charge are proportional to the size of the charge.
b. Field lines cannot intersect.
c. Electric field lines are parallel to equipotential lines.
d. Field lines must begin on (point away from) a positive charge and end on (point toward) a
negative charge.
5. What is the most general formula for phase difference between two mechanical waves?
a.
b.
c.
d.
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6. Which one of the following is NOT a condition for choosing a symmetric Gaussian Surface.
a. Electric field is parallel to the surface.
b. The angle between vectors
and
is 0º (or 180º) and
is uniform.
c. Electric field is zero around the surface.
d. The angle between vectors
and
is 45º.
7. Which of the following best describes longitudinal and transverse mechanical waves?
a. The velocity of the wave itself as compared to the velocity of an element of the medium is
perpendicular for a transverse wave and parallel for a longitudinal wave.
b. The velocity of the wave itself as compared to the velocity of an element of the medium is
perpendicular for a longitudinal and parallel for transverse wave.
c. A transverse wave requires a medium where as a longitudinal wave does not.
d. A longitudinal wave requires a medium where as a transverse wave does not.
8. Captain Picard of the star-ship Enterprise tells his security chief to turn on the shields. These
shields are a field just like the fields we've discussed (electric and magnetic). Which of one of the
following is true of the field.
a. It depends on test particles only.
b. It is a property of the space only (treating the Enterprise as the source).
c. It is a property of the space and depends on test particles.
d. None of the above.
9. As a physics 1051 student you might appreciate a hidden (but not so subtle) reminder in the final
exam itself to remember to pay attention to certain details of your workings. On an unrelated
note, which one of the following uses correct vector notation?
a.
b.
c.
d.
10. If you have two pieces of Polaroid above a light source (e.g. on top of the light of a doc cam in
C-3033) and you notice that as your rotate them at some point a black spot forms (i.e. intensity of
light passes through it is zero). This occurs when the angle between transmission access of the
analyzer and the polarizer is
a.
b.
c.
d.
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Long Answer Questions [10 marks each, 80 marks total]
1. A mass on a spring is oscillating in simple harmonic motion. Its motion is described by the
equation
where the phase constant is
. The spring has a
spring constant of
A. For the
i.
ii.
iii.
.
spring find the following
The mass of the object on the spring.
Given that the amplitude is
, find the velocity at
.
If you were told that everything about the mass remained the same but the mass
started at a different location at
, what parameter would change and why?
B. A string of length
is now attached to the mass, as in the diagram below, so that
the oscillating creates a standing wave on the string.
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i. Sketch the 3 harmonic of the wave and label nodes, antinodes and ends as being
fixed or free.
ii. Find the wavelength.
iii. Very briefly describe the difference between a travelling wave and a standing
wave.
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2. Mechanical waves are very similar to EM waves.
A. Briefly state the main difference between mechanical waves and electromagnetic waves.
B. Given that a function for for the electric field is defined by
,
do the following.
i. Using the equation for speed of a wave, derive the formula for the speed of a wave
in terms of angular wave number and angular frequency .
ii. Show that
satisfies the linear wave equation. [Hint: Show that the left
hand side of the linear wave equation is the same as the right hand side.]
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3. You have the following point charges as indicated in the diagram. The charges have values
,
and
.
A. Find the total electric field at the position
marked on the diagram.
B. What is the potential at the same position?
C. Ignoring
now, what is the electrical potential energy in the
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,
system?
4. You have a continuously and uniformly charged rod with
.
A. Find the potential at the origin due to the rod.
B. Before deciding not to bother calculating it, you consider how you would find the electric
field due to the rod.
i. Without doing any calculations, state the value for the x component of the electric
field at the origin and provide an explanation.
ii. State the direction of the electric field at the origin using a unit vector, again
without any calculations.
iii. Briefly explain why the reasoning in the two previous question parts do not apply
for calculating the electric field at
.
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5. You have a conducting spherical shell of charge
that is sitting inside a conducting
square shell (in static equilibrium) which has a charge of
as indicated in the
diagram. Also, you've parked your peddle bike, which has a charge of
, inside the
square shell.
A. What is the electric field at a radius
(centered around the center of the spherical
shell) just outside outside the spherical shell?
B. You are curious where all the charge on the square shell is located.
i. Find the charge on the inner surface of the square shell.
ii. Find the charge on the outer surface of the square shell.
C. What is the electric flux through a sphere of radius
spherical shell (i.e. just outside the spherical shell)?
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centered on the centre of the
6. It is possible for a current carrying wire to both feel a magnetic force and create a magnetic field.
A. Given that there is a magnetic field
, what is the magnetic force on;
i. an electron traveling whose velocity is in the x-y plane at an angle of
the x-axis and has a magnitude of
?
ii. a bunch of electrons in a wire of length
with a current of
pointing along the x-axis?
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B. Penny can't believe that it is Friday night and Sheldon Cooper and his buddy Leonard are
using Ampere's Law on their white board to find the magnetic field outside a wire. Follow
their lead and derive the magnitude of the magnetic field outside the wire with current
at a distance away from the wire. [Hint: The final answer is on your formula sheet.]
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7. A uniform magnetic field
along a set of rails separated by
the rails.
is directed into the page. Two rods are free to be pulled
. There is no friction between the rod 1 and 2 and
A. A conducting rod (rod 1) is pulled horizontally with constant force of magnitude
whose vector is indicated in the diagram. The rod moves with constant
velocity
.
i. Using Faraday's Law, calculate the magnitude of the induced emf around the loop
in the figure.
ii. Find the direction of the current and briefly explain your answer.
B. Explain what would be different if rod 2 was also pulled in the same direction with the
same velocity. Comment on the emf and current.
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8. You are considering light and the different ways it interacts constructively and destructively with
different types of barriers.
A. If the light hits a double slit with a slit spacing of
, the first bright spot above the
central spot on the screen will be
from the central bright spot as indicated in the
diagram. The angle from the horizontal to this fringe is
i. Find the path difference of the two rays (see diagram) from each slit to the first
bright spot above the central fringe.
ii. In general, sate what the phase difference is for the following; middle fringe (also
known as zeroth order or central maximum), the first bright fringe away from the
central fringe (also known as first order), the second bright fringe away from the
central fringe (second order).
iii. Starting from the general definition of phase difference, simplify the formula for
the phase difference for this case. (Hint Both rays have a common source.)
iv. Find the wavelength of light.
B. Now light, this time of
, hits a thin film. The phase change due to their
traveling (ray 2 has traveled and extra distance through the film) is
and the distance
through the film is approximately
where the thickness is
.
i. State what the total phase change due to reflection is given that
,
and
. Provide an explanation.
ii. What is the total phase change?
iii. Will there be constructive interference, destructive interference or neither?
C. Derive a formula for critical angle for the case of total internal reflection. [Hint: Snell's
Law]
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