Term 2 Exam - April 18, 2016

Name:

Student Number:

Bamfield Number:

Questions 1-24:

Multiple Choice:

1 point each

Questions 25-30:

Long answer:

24 points total

Formula sheet at the

back

Question 1: Please refer to the picture above. What is the strength of the electric

field at point B relative to point A?

A) Field at B is 4 times that at A.

B) Field at B is 2√2 times that at A.

C) Field at B is 2 times that at A.

D) Field at B is √2 times that at A.

E) Field at B is 1/√2 that at A.

F) Field at B is 1/2 that at A.

G) Field at B is 1/(2√2) that at A.

H) Field at B is 1/4 that at A.

Question 2: Please refer to the same picture. What is the strength of the electric

potential at point B relative to point A (assuming the potential is 0 at infinity)?

A) Potential at B is 4 times that at A.

B) Potential at B is 2√2 times that at A.

C) Potential at B is 2 times that at A.

D) Potential at B is √2 times that at A.

E) Potential at B is 1/√2 that at A.

F) Potential at B is 1/2 that at A.

G) Potential at B is 1/(2√2) that at A.

H) Potential at B is 1/4 that at A.

Question 3: A dipole is held next to an infinite plane of charge. What happens

when the dipole is first released?

A) It rotates counterclockwise and moves to the right.

B) It rotates counterclockwise and moves to the left.

C) It rotates counterclockwise.

D) It rotates clockwise.

Question 4: Two charges rest next to an infinite

plane of charge as shown. Using the Answer

Octopus below, indicate in what direction the

electric field is pointing at the location indicated

above.

Question 5: The diagram below shows equipotential lines from some charge

configuration. Which of the points A, B, C or D has the strongest electric field?

Question 6: The simulation above shows the path an electron takes as it travels in

a solid. It starts in the circle in the top right, and ends at the circle in the bottom

left. What is true about the electric field that this electron experiences?

A) The electric field points in the direction.

B) The electric field points in the direction.

C) We can’t determine what direction the field is in.

Question 7: Current flows from two wires, A and B, into a third wire C as shown

above. Assume the wires all have the same thickness. What can we say about the

electric field in wire A compared to wire C?

A) The electric field is larger in wire C than A

B) The electric field must be the same in both wires

C) The electric field is smaller in wire C than A

Question 8: The two parallel plate capacitors are

drawn to scale (capacitor A has four times the area

and twice the separation as B). If we hook each

capacitor up to the same voltage V, what can we say

about the charges QA and QB on each capacitor?

A) QA = 4QB

B) QA = 2QB

C) QA = QB

D) QA = QB/2

E) QA = QB/4

Question 9: Your new “Fun With Magnets” kit arrives from Amazon. You open the

box and find three metallic cylinders stuck together as shown. If you remove cylinder

number 2, the first and third cylinders don’t stick to each other at all. What will happen

if you put cylinder number 2 back between 1 and 3, but in the opposite orientation?

A) Cylinders 1 and 3 will be repelled from number 2.

B) Cylinders 1 and 3 will be attracted to number 2, just like before.

C) Cylinder number 2 will flip itself around.

D) No attraction or repulsion will be noticed

Question 10: Betty wants her model of the Earth to have a magnetic field similar to

the Earth’s magnetic field, so she adds some current carrying wire to the model. Which

of the following configurations will produce a magnetic field most similar to the

Earth’s?

Question 11: A magnetic will stick to certain objects that are not themselves magnets

because

A) the magnet causes a current to flow in the object so that it begins to behave like a

magnet.

B) the magnet causes electric dipoles in the object to rotate and align with each other

resulting in a net attraction to the magnet.

C) the magnet causes electron spins in the object to align each with each other. These

electrons behave as little magnets which add up to make the object behave like a

magnet.

D) the magnet causes the positive and negative charges to flow to opposite ends (since

the object must be a conductor). This results in dipole-dipole type attraction with the

magnet.

Question 12: A positively charged particle has an initial

velocity as shown in a region where the magnetic field is

uniform and in an upwards direction. The subsequent path

of the particle will be

A) a circle, with the initial deflection of the particle out of the

page.

B) a circle, with the initial deflection of the particle in the

upwards direction.

C) an upward helix.

D) a downward helix.

E) a straight line.

Question 13: In the picture to the right, the conducting ring is held

in place, but the magnet (initially stationary) is allowed to fall. As

the magnet falls,

A) A clockwise current (looking from the top) will be

induced in the ring.

B) A counterclockwise current (looking from the top) will

be induced in the ring.

C) No current will be induced.

Question 14: In the previous question, when the magnet has fallen to twice its initial

distance from the ring, we can say that the flux through the ring from the magnet’s

field will be

A) Approximately double the initial flux

B) Approximately the same as the initial flux

C) Approximately half the initial flux

D) Approximately one quarter the initial flux

E) Approximately one eighth the initial flux

Question 15: Each of the three rectangular loops above carries the same current and

sits in the same uniform magnetic field pointing to the right. Rank, from largest to

smallest, the magnitudes of the torques on the three loops

A) 1=2>3 B) 1>2>3 C) 2>3>1 D) 2>1>3 E) 3>1=2 F) 3>2>1

Question 16: The conducting loop shown

at the right rotates at a constant angular

velocity with the left side initially rotating

out of the page as shown. Which of the

graphs below best represents the induced

current in the loop starting from the time

shown in the picture?

Question 17: The picture above shows a snapshot graph taken at t = 0. Which graph

below best represents the history graph at the position of the duck?

Question 18: You’re playing your guitar and you want make your low E string an

octave higher (doubling the frequency). What is the ratio of the new tension to the old

tension Tnew/Told?

A) 4

B) 2

C) √2

D) 1

E) 1/√2

F) 1/2

G) 1

Question 19: The two speakers are emitting a sound of

170 Hz out of phase from each other. What type on

interference is occurring at the point on the right?

A) Very close to constructive

B) Very close to deconstructive

C) In between constructive and deconstructive

Question 20: The pictures above represent the photons in two beams of light. If each

photon shown has the same energy, we can say that the second beam gives a light

wave with

A) the same wavelength as the first but double the power/intensity.

B) half the wavelength as the first but the same power/intensity.

C) twice the wavelength of the first but half the power/intensity.

D) the same wavelength as the first but half the power/intensity.

E) half the frequency as the first and half the intensity.

Question 21: The wavefunction above represents an electron (mass 9 ×10-31kg)

travelling to the right. Which of the following is closest to the distance that this

particle is expected to travel in 1μs = 10-6s?

A) 1 μm B) 1 mm C) 1 m D) 300 m

Question 22: For the wavefunction above, which of the pictures below best represents

the shape of the wavefunction at some (significantly) later time

Question 23: Mario and Luigi have identical nanoscale wires each containing a single

electron each with the same wavefunction as shown. If they both measure the location

of their electron, the chances that they will find the same result to an accuracy of 1nm

are

A) 100% B) 50% C) 25% D) Almost zero

Question 24: Two electrons with identical wavefunctions each approach a slit. If the

first slit is significantly narrower than the second, as shown, we would expect that after

the electrons pass through the slits, the wavefunction for the first electron will

A) Travel faster than the wavefunction for the second

B) Travel slower than the wavefunction for the second

B) Spread out faster in the horizontal direction compared with the second electron’s

wavefunction

C) Behave in precisely the same way as the second electron’s wavefunction

D) Spread out slower in the horizontal direction compared with the second electron’s

wavefunction

Question 25: a) Calculate the potential at point A in the circuit shown (the potential at

the lower left is defined to be 0V). (3 points)

b) What is the potential at point A if the 4.0 Ω resistor in the circuit above is

replaced by a capacitor and the circuit is left to run for a very long time? Explain.

(1 point)

Question 26:

Two wave sources are in phase waves and produce a sound with the same frequency.

The BFG (Big Friendly Giant) is located 3 meters away from the line connecting the

sources, as shown above. What is the maximum possible wavelength for the waves, if

the BFG hears no sound at the point? (Assume that the amplitudes of the waves from

the two sources are the same at the BFG’s ear) (3 points)

Question 27:

A circuit is set up with two 30cm vertical wires (mass

1g, resistance 0.01Ω) suspended between horizontal

wires (assumed to have no resistance), so that the

vertical wires are free to move. If these vertical wires

are initially held in place 5cm apart until the circuit has

a steady current and then released, they are observed to

accelerate away from each other at 0.1m/s2. Based on

this observation, determine the voltage of the battery.

You may assume that the wires are close enough

together so that the magnetic field at one wire is

approximately the same as if the other wire were

infinite.(4 points)

Question 28:

The Science One teaching team decides to

generate additional revenue to supplement the

program budget by selling some official Science

One merchandise. One of the top sellers is the

electrostatic Tippy-Chris toy (a registered

trademark of Science One Enterprises).

The toy includes a positively charged

Chris head (Q = 1mC, mass = 10g)

attached to a thin rod (length L = 10cm,

mass 20g).

The rod is attached loosely at the other end to a line of charge, so that the Chris

head end can move around freely.

a) If the Tippy-Chris is set to rest, the rod leans at an angle of θ = 30 degrees with the

vertical as shown. Determine the charge density λ for the line of charge. (You may

approximate the Chris head to be a point charge/mass). (3 points)

b) Now the Tippy-Chris is moved into a vertical position and released. The Tippy

Chris bounces back and forth from left to right between some angle –θ and angle θ. Making use of energy conservation, determine the angle θ. (2 points)

Question 29: The first picture below shows the wavefunction for an electron inside a

wire moving to the right towards the end of the wire (as depicted in the second

picture). The potential energy inside the wire is -2eV, while the potential energy

outside the wire is 0eV. If the electron initially has enough energy to escape the wire

(say 1eV total energy), sketch the electon’s wavefunction after it has had time to exit,

on the axes in the third picture. Explain how the various features of the later

wavefunction compare with those in the initial wavefunction, explaining your

reasoning. (4 points)

Question 30:

Sally is a bit of a worrier. Her kids like to ride their bikes up and down

the street, but she always thinks that they are going way too fast. So

Sally invents a new kind of bike with a big conducting square (1m by

1m, net resistance 0.1 Ω) around the rider. She installs some big

electromagnets under the road in front of her house that can

produce a uniform upwards magnetic field. If her son and his

bike together have a mass of 70kg, and if the bike is

travelling at 10 m/s when it enters the field, how strong a

magnetic field does Sally need in order to produce an

acceleration of -1m/s2 due to the effects of magnetic

induction? (3 points)

b) BONUS (1 point + fame and glory) What will be the final velocity of the bike

once the conducting loop is entirely in the magnetic field?

FORMULA SHEET

a = dv/dt v = dx/dt

F = ma a = v2/R

Fr = -dU/dr W = -ΔU = -∫ F∙dr

F = qE U = q V

Er = -dV/dr ΔV = -∫ E∙dr

E = kq/r2 E = λ / (2 π ε0 r) E = η/(2ε0) E = 2kp/r3

p = qs V = Ed

k = 9 × 109 N m2/C2 ε0 = 8.85 × 10-12 C2/(N m2) e = 1.602 × 10-19 C

F = qE + q v x B F = I l x B τ = μ x B μ = I A

B = μ0/(4π)q v × r / r3 B = μ0/(4π)I ds × r / r3 B = (μ0 / 2 π) I/d B = μ0 (N/L) I

B = (μ0/4π) 2 μ /z3 μ 0 = 4 π × 10-7 Tm/A

V = IR C = Q/V P = IV C = ε0A/d

R = ρL/A σ = nee2τ/m = 1/ρ vd = e τ E/m I = e ne Avd

Q(t) = Q0exp(-t/RC)

ε = |dΦm/dt| Φ = B∙A = BAcos(θ)

∮ ∙ = -dΦm/dt

λ f = v

E = hf p = h/λ Δx Δp = h/(4 π) h= 6.6 × 10-34 Js