Science One Term 2 Physics Exam April 24, 2014

Name:

Student Number:

Bamfield Number:

Questions 1-26: Multiple Choice: 1 points each

Problems 1-6: Long answer: 26 points total

Multiple choice answers:

Formula sheet at the back (you can remove it…carefully!)

Question 1: In a permanent magnet, configurations in which more of the electron

spins are aligned with each other have

A) Higher entropy but lower energy

B) Higher energy but lower entropy

C) Both higher energy and higher entropy

D) Both lower energy and lower entropy

Question 2: A certain type of

which can be straight or bent 180° back on itself.

entropy for the set of configurations with exactly two kinks

A) kB ln(4)

B) kB ln(6)

C) kB ln(8)

D) kB ln(12)

E) kB ln(16)

Question 3: If the polymer molecules have the same energy regardless of length,

typical long polymer molecule observed at random in a lar

molecules is likely to have

A) Much less than half of its joints kinked

B) Roughly half of its joints kinked

C) Most of its joints kinked

D) None of the above: these are all eq

Question 4 : Three charges lie on the corners of a square as shown below. Which

arrow is the closest to the direction of the electric field at the upper right hand corner

of the square?

In a permanent magnet, configurations in which more of the electron

spins are aligned with each other have

A) Higher entropy but lower energy

B) Higher energy but lower entropy

higher energy and higher entropy

D) Both lower energy and lower entropy

A certain type of polymer molecule has a series of many “joints,” each of

which can be straight or bent 180° back on itself. In a small polymer with 4 joints, the

entropy for the set of configurations with exactly two kinks (such as the one shown)

If the polymer molecules have the same energy regardless of length,

polymer molecule observed at random in a large collection of such

A) Much less than half of its joints kinked

B) Roughly half of its joints kinked

D) None of the above: these are all equally likely

Three charges lie on the corners of a square as shown below. Which

arrow is the closest to the direction of the electric field at the upper right hand corner

In a permanent magnet, configurations in which more of the electron

polymer molecule has a series of many “joints,” each of

with 4 joints, the

(such as the one shown) is

If the polymer molecules have the same energy regardless of length, a

ge collection of such

Three charges lie on the corners of a square as shown below. Which

arrow is the closest to the direction of the electric field at the upper right hand corner

Question 5: The electric field at two points in space is shown below. At what position

is the charge located that generates this field? Assume that the vertical tick marks are

equidistant.

Question 6: In a special universe where the electric field from a point c

1/r3 law, what is the distance dependence of the electric field far away from a dipole

made of these special charges?

A) 1/r

B) 1/r2

C) 1/r3

D) 1/r4

E) 1/r5

Question 7: A dipole is held next to a wall (in space). What do we expect to happen

the moment after the dipole is released

A) rotate counterclockwise

B) rotate counterclockwise and move left

C) rotate counterclockwise and move right

D) rotate clockwise

E) rotate clockwise and move left

F) rotate clockwise and move right

G) nothing

Question 8: Part of a wire with a shape shown

it. Which region has the greatest electric field?

A) A

B) B

C) C

D) A, B, C, have the same electric field strength

The electric field at two points in space is shown below. At what position

is the charge located that generates this field? Assume that the vertical tick marks are

In a special universe where the electric field from a point c

law, what is the distance dependence of the electric field far away from a dipole

made of these special charges?

A dipole is held next to a wall (in space). What do we expect to happen

dipole is released (ignoring gravity)?

unterclockwise and move left

nterclockwise and move right

tate clockwise and move left

rotate clockwise and move right

Part of a wire with a shape shown has a uniform current running through

it. Which region has the greatest electric field?

A, B, C, have the same electric field strength

The electric field at two points in space is shown below. At what position

is the charge located that generates this field? Assume that the vertical tick marks are

In a special universe where the electric field from a point charge obeys a

law, what is the distance dependence of the electric field far away from a dipole

A dipole is held next to a wall (in space). What do we expect to happen

current running through

Question 9: In the circuit shown below

difference from A to B?

A) -5/2 V

B) -2 V

C) 0 V

D) +2 V

E) +5/2 V

Question 10: A parallel plate capacitor is in series with a 9 Volt battery and a resistor.

If the plates of the capacitor are moved physically further apart. What happens to the

charge on the capacitor?

A) It decreases

B) It stays the same

C) It increases

Question 11: Two points, A and B, are the same

distance from a line of charges. The work done to move

a negative charge from point A to point B

gravtity) is

A) positive

B) zero

C) negative

Question 12: In static equilibrium, the potential difference between two points inside

a solid piece of metal

A) is zero because metals block electric interactions

B) is zero because the electric fie

C) is non-zero if the piece of metal is not sphe

D) is non-zero if there are charges on the surface

E) is non-zero for reasons not given above.

F) is zero for reasons not given above.

In the circuit shown below with the switch open, what is the potential

A parallel plate capacitor is in series with a 9 Volt battery and a resistor.

If the plates of the capacitor are moved physically further apart. What happens to the

Two points, A and B, are the same

distance from a line of charges. The work done to move

a negative charge from point A to point B (ignoring

In static equilibrium, the potential difference between two points inside

is zero because metals block electric interactions�

is zero because the electric field is zero inside the metal

zero if the piece of metal is not spherical

zero if there are charges on the surface of the metal

or reasons not given above.�

is zero for reasons not given above.

, what is the potential

A parallel plate capacitor is in series with a 9 Volt battery and a resistor.

If the plates of the capacitor are moved physically further apart. What happens to the

In static equilibrium, the potential difference between two points inside

Question 13: The entire region shown

potential difference VA – VC is

A) ���

B) ���

C) ���

D) ���

E) ��√�� � ��

F) �√�� � �� G) zero

Question 14: Two particles with opposite charges pass each other as shown in the

diagram. At the instant shown, the magnetic force on the top particle from the bottom

particle will be

A) Upwards

B) Downwards

C) To the left

D) To the right

E) Into the page

F) Out of the page

G) Zero

Question 15: Current flows through the wires A and B in the directions shown. The

magnetic field at the point shown on the right points

A) To the right

B) To the left

C) Upwards

D) Downwards

E) Up and to the left

F) Down and to the left

G) None of the above: the field is zero

The entire region shown is filled with a uniform electric field. The

is

Two particles with opposite charges pass each other as shown in the

diagram. At the instant shown, the magnetic force on the top particle from the bottom

Current flows through the wires A and B in the directions shown. The

magnetic field at the point shown on the right points

G) None of the above: the field is zero

is filled with a uniform electric field. The

Two particles with opposite charges pass each other as shown in the

diagram. At the instant shown, the magnetic force on the top particle from the bottom

Current flows through the wires A and B in the directions shown. The

Question 16: Four small magnets are in a uniform magnetic field that points in some

direction in the plane of the page. If the torques on the magnets are as shown (in units

of 10-3

N m with positive = ), in which direction A-H shown above does the

magnetic field point?

Question 17: A charge is moving in a uniform

magnetic field with initial velocity as shown.

Which of the following best represents the

subsequent trajectory of the particle (note: D

and E lie in a plane)?

Question 18: The shaded region contains a magnetic field

pointing into the page. If the three rectangular wire loops

are identical apart from their position and orientation, and

all three are moving to the right with the same speed, rank

the induced currents in the loops.

A) 1 = 2 = 3

B) 1 = 2 < 3

C) 3 < 1 < 2

D) 1 = 2 > 3

E) 2 < 1 < 3

F) None of the above

Question 19: A copper ball is falling directly downwards to the

Earth near Vancouver. We can say that positive and negative

charges will build up on opposite sides of the ball, with positive

charge on the

A) North side B) South side C) East side D) West side

E) Top side F) Bottom side

Question 20: A rectangular loop of current is lifted off a magnet as

shown. Looking from the top, there will be

A) A clockwise current in the loop

B) A counterclockwise current in the loop

C) No current in the loop

Question 21: The plot above show the snapshot graph for a wave pulse moving to

the right on a string with speed 2 m/s. Which of the graphs below represent the history

graph for some point on the string?

Question 22: The plot above shows the history graph for a sinusoidal wave. Which of

the plots below shows the history graph for a sinusoidal wave with double the

wavelength but the same velocity.

Question 23: In the picture below, sound with wavelength 2m is coming from the two

in-phase sources. If the grid squares are 1m by 1m, at which of the marked points will

destructive interference occur?

Question 24: Light will ionize a gas of hydrogen atoms only for sufficiently large

A) wavelength

B) frequency

C) velocity

D) intensity

E) More than one of the above is correct

Question 25: After a measurement of the position of an electron (mass 9×10-31

kg), its

wavefunction is localized to a region of size 10-7

m. One second later, we can say that

the least possible uncertainty in position is closest to

A) 6nm B) 6μm C) 6mm D) 6m E) 600m

Question 26: The wavefunctions below represent an electron traveling towards the

end of a wire. For which wavefunction is the electron most likely to escape the wire?

Problem 1: The two wavefunctions shown above represent electrons travelling to the

right. Describe qualitatively how and why the evolution of these two wavefunctions

will differ from each other, explaining your answers using relevant physical

principles or equations. (4 points)

Problem 2: On ƁeƮƮƴ’s home planet Phllaat!, the surface of the planet has a varying

charge density, and the people of Phllaat! have special antennae that help them

measure this charge density (it’s often very very foggy on Phllaat!, and measuring the

charge density helps them navigate). ƁeƮƮƴ’s antennae each have a ball of mass 0.1

gram and charge 20nC at the end of a 1cm long flexible thread. If ƁeƮƮƴ’s antennae

always make an angle of 120 degrees with each other just outside her house, what is

the charge density on the ground there? (5 points)

(Note:the gravitational acceleration on planet Phllaat! is g=10m/s2)?

Problem 3: Solids typically expand when the get hotter. Enid would like to

determine the how much bigger her favorite piece of copper is when she is holding it

compared to when she is not. So she sets up a 650nm laser and some mirrors attached

to either end of the copper so that the laser beam splits up and recombines as shown.

As the copper heats up, Enid finds that the intensity of the combined beam at the

detector gets larger and smaller repeatedly. Between room temperature (20C) and her

body temperature (37C), the signal gets brighter and darker 18 times. Explain why

the signal gets brighter and darker and determine by what percent length of Enid’s

copper increased if it is initially 2cm long. (4 points)

Problem 4: One day, Mr. Zucchini is swinging back and forth on his rope without

friction. Mr. Zucchini has recently taken off some sweaters, causing him to have a net

electric charge. At some point, a uniform magnetic field turns on in the direction

perpendicular to the plane of the swing and starts to increase in magnitude. Above

some particular magnetic field strength, Mr. Zucchini starts to feel a “jump” at the

bottom of his swing when travelling from left to right, but not when travelling from

right to left.

a) Explain why this phenomenon occurs. (2 points)

b) If Mr. Zucchini has charge 10mC and weighs 100 g, and if his rope is 2m long with

an initial angle of 45 degrees, at what magnetic field strength will he start to feel the

jump? (2 points)

Problem 5:

In the circuit, the battery voltage is V = 12 V, the

resistors have resistance R1 = 1 Ω, R2 = 2 Ω, R3 = 3

Ω, and the capacitor has a capacitance C = 10 mF?

a) Switch A is closed. Afterwards, what is the voltage

across resistor R2? (2 points)

b) If switch B is now closed, sketch how the voltage across resistor R2 changes as a

function of time, starting from just before switch B is closed. (1 point)

c) After a long time, switch A is opened again. What is the charge on the capacitor as

a function of time, starting from t=0 when switch A is opened? (2 points)

Problem 6:

When Sally tells her spaghetti fork idea

to her friend Harry, Harry expresses a

concern that the torque from the motor

(which produces angular acceleration)

will cause an ever-increasing angular

velocity that could be harmful to the

user and their family (either by direct

impalement, or by causing a tornado).

Sally quickly points out that Harry (a

chemist, perhaps?) has neglected to take into

account the effects of electromagnetic

induction (not to mention friction).

a) Explain how/why even in the absence of friction, induction effects will ensure that

the loop does not spin faster than some maximum angular velocity. (2 points)

(Recall that the torque, which is due to magnetic forces on the current going through

the loop, is always in the same direction, since the unit is designed so that current

through the loop switches direction twice per spin).

b) Assuming a single loop, if the current in the loop is I=1A, the resistance in the loop

is R=1Ω, the area of the loop is A = 10cm, and the magnetic field is B = 1T, estimate

the largest angular speed that will be attained in the absence of friction. (2 points)

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 = η/(2ε0) E = 2kp/r

3 p = qs

Flux = Qenc/ε0

k = 9 × 109 N m

2/C

2 ε0 = 8.85 × 10

-12 C

2/(N m

2) 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 / r

3 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

R = ρLA

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

S = kB ln(N)