MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF PHYSICS & PHYSICAL OCEANOGRAPHY
Physics 1051 Spring 2020
Instructor: Kelly Shorlin and Anand Yethiraj
Final Exam
(Dated: Monday, August 10, 2020)
INSTRUCTIONS
1. Do all questions. Each question in section 1 is worth 10 points. Each question in section 2 is worth 20 points. Marks are
indicated in the left margin. Section 1 contains 40 points, and section 2 contains 60 points.
2. You may use a calculator. You may use a computer in order to do an integral in Wolfram Alpha (if you choose). You
may use the course text book, as well as the course instructors’ lecture notes. All other aids are not allowed.
3. In order to correct answers, strike out the material to be replaced with a neat line.
4. If something is not clear, ASK me (AY).
5. The official time slot for the Final exam 4:00pm - 6:30pm. The expanded time window is 4 pm to 9pm. I will be in the
Online Room during this time, and will also be reachable by email throughout. Exams must be submitted through the
Assignments module before 9pm. Exams emailed to me will not be accepted!
6. You must time yourself – turn off the timer if you need to take a break – and stop yourself at 2 hr 30 minutes. There
will be no invigilation, you are being trusted to be honest.
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SECTION 1
1. [10 points] Waves
(a) What is the difference between the transverse velocity and the wave speed of a traveling wave?
(b) A left travelling wave on a string has wavelength 0.333 m and wave speed 100 m/s. The maximum transverse
velocity is 0.500 m/s. The point on the string at x=0 has initial height 0.200 mm and is moving downward.
i. Write the equation of motion for the above left traveling wave. [Hint: The answer will require you to
figure out all the numerical values.]
ii. Find the equation for transverse velocity for this wave. Obtain a value for the transverse velocity at
t = 1ms.
2. [10 points] Electric potential and electric fields
(a) The electric potential along the y axis is V = 100
p
1 + y 2 volt.
i. Write down an expression for the y component of the electric field, Ey .
ii. What is Ey at y = 0 m
iii. What is Ey at y = 1.5 m?
(b) A 1.0-cm-diameter metal ball has 2 × 1010 excess electrons.
i. What is the ball’s electric potential?
ii. How much work is required to remove 1 electron from this ball?
3. [10 points] Magnetic forces and torques A square loop of wire is situated in a region of uniform magnetic
field with its diagonal parallel to the magnetic field lines as shown in Figure 1. A current of 2.0 A circulates
counterclockwise around the loop. Each side of the square is 1.7 m long. The axis system is as shown with the
~ = 2.5ĵ T.
z axis out of the page. The magnetic field is B
FIG. 1: A square loop in a changing magnetic field.
(a) What is the magnetic force on the side ab? Give your answer in unit vector notation.
(b) What is the magnetic moment µ
~ of the loop? State your answer in unit vector notation.
(c) What is the torque ~τ on the loop? State your answer in unit vector notation.
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4. [10 points] Magnetic fields and induced currents A square loop of wire, with sides of 0.25 m and a
resistance of 333 Ω, is placed in a region where there is a magnetic field perpendicular to the plane of the loop
and out of the page as shown in Figure 2. The magnetic field increases linearly with time and its magnitude is
given by B = 0.04t where t is in seconds and B is in Tesla. What is the magnitude and direction (clockwise or
counterclockwise) of the resulting current?
FIG. 2: A square loop in a changing magnetic field.
SECTION 2
5. [20 points] Electric Fields
FIG. 3: Electric field due to a ring of charge and a point of charge
A long rod is shaped into a ring with radius R = 10.0 cm. This ring lies in the y-z plane. The ring is carrying
charge Q = 25.0µC and a point charge q = −5.00µC is held at distance R from the centre of the ring (along the
+x direction) as shown in Figure 3. Point P is distance 2R from the centre of the ring (along the +x direction).
(a) Obtain an expression, in terms of the variables Q and R, for the electric field at P due to the ring alone, by
integrating each infinitesimal contribution to the field over the ring. Report your answer using unit vector
notation. Do not plug in the values for Q or R yet!
(b) Evaluate this expression at point P using the provided values for Q and R. Report your answer using unit
vector notation.
(c) Write down the expression for the electric field at P due to the point charge q alone. Evaluate this expression
at point P. Report your answer using unit vector notation.
(d) Find the net electric field at point P. Report your answer using unit vector notation.
(e) If the point charge q were released and could move freely, describe in words its motion (1 sentence only!).
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6. [20 points] Gauss’ law An uncharged box with thick conducting sides contains two charges, q1 = 5µC and
q2 = 5µC. The charge q2 is enclosed by an uncharged spherical conducting shell as shown in Figure 4.
FIG. 4: Electric field due to a ring of charge and a point of charge
Provide 1-sentence justification to each answer below. Draw Gaussian surfaces to make your
point.
(a) What is the electric field in the region of bulk conductor between the inside and outside surface of the box?
(b) What is the total charge on the inside surface of the spherical conducting shell?
(c) What is the total charge on the inside surface of the box?
(d) What is the total charge on the outside surface of the box?
(e) Where on the outside surface of the box would you expect to find the highest surface charge density, and
why?
7. [20 points] Magnetic field of a current
FIG. 5: Electric field due to a ring of charge and a point of charge
(a) What is the magnetic field direction at at the center of the circular arc (point P), due to
i. segment 1
ii. segment 2
iii. segment 3
of the wire shown in Figure 5. Give a brief justification, using vector sketches to support your answer, in
each case.
~ at the center of the circular arc
(b) Obtain an expression, in terms of R, θ and I, for the magnetic field B
(point P) in Figure 5. Write your answer in unit vector notation.
(c) For θ = 2π, the arc of wire would be a current loop. Does your expression above give the right expression
for a current loop?
(d) For a current of 1.0 A, angle θ = 60◦ , and R = 10 cm, obtain the magnetic field (in unit vector notation).