Physics 122 Final Exam

Physics 122 Final Exam - 24 April 1997

1.

``QUICKIES'' [16 marks - 2 each]

(a)

The basic building blocks of nature are 6 quarks and 6 leptons. Name two of the leptons.

(b)

The main source of energy of our sun is a set of nuclear reactions which convert hydrogen to form the element .

(c)

Which of the following has the dimensions of time? [encircle one]

(i) LR (ii) CR (iii) LC (iv) 1/LR (v) 1/RC (vi) 1/LC

(d)

In British Columbia we average 625 deaths per year from a certain kind of cancer. For any given year the number of deaths would be expected to lie within $\pm$ % of this average nineteen times out of twenty.

(e)

For an AM radio we have a fixed inductance, L, and a variable capacitance, C, to tune to the stations of the AM band. If $C = 3.0 \times 10^6$ F for the upper end of the band (1600 kHz), what value of C tunes to the lower end of the band (530 kHz)?

(f)

We have a system of 37 slits which are illuminated to form a diffraction pattern. How many little intensity ``bumps" are there in between adjacent principal maxima?

(g)

For an ideal gas the pressure and temperature are directly related to one of the following velocities of the gas molecules: [underline one]

(i) most probable velocity; (ii) average velocity; (iii) root-mean-square velocity; (iv) maximum velocity.

(h)

Maxwell completed the laws of electromagnetism by adding a crucial extra term to which of the following: [underline one]

(i) Gauss' Law for electricity; (ii) Gauss' Law for magnetism; (iii) Faraday's Law; (iv) Ampère's Law.

2.

ELECTROMAGNETIC FORCE: [10 marks] In a certain region of space we have an electric field $\vec{E}$ and a magnetic field $\vec{B}$ :

$\begin{displaymath}\vec{E} = [7\hat{\imath} + 4\hat{\jmath} + 6\hat{k}] \hbox{\r . . . . . . } = [-3\hat{\imath} - 4\hat{\jmath} + 10\hat{k}] \hbox{\rm ~T} \end{displaymath}$

If an electron is moving in this region with a velocity $\vec{v} = [2\hat{\imath} + 3\hat{\jmath}]$ m/s,
what is the instantaneous force (full vector form by components) on the electron? ( $e = 1.6 \times 10^{-19}$ C).

3.

CAPACITANCE: [14 marks, 8 for a) and 6 for b)] We attach a battery, $\varepsilon = 12$ volts, to 9 equal capacitances in a circuit as shown, with $C_1 = C_2 = C_3 = C_4 = C_5 = C_6 = C_7 = C_8 = C_9 \equiv C = 9.0 \times 10^{-6}$ F.

(a): What is the amount of charge which flows from the battery to fully charge the system of capacitors?
(b): What is the charge on each of the capacitors?

Sorry, Figure unavailable!

4.

RL CIRCUIT: [14 marks, 4 for a) & d), and 3 for b) & c)] We have used a battery to build up a magnetic field of B = 0.6 T inside a superconducting coil 0.5 m long and 0.02 m² in cross-sectional area. Now we suddenly switch off the battery and put the coil in series with a resistance of 120 $\Omega$ . We observe that it takes 3.6 milliseconds (ms) for the field in the coil to drop to 0.1 T. ( $\mu_0 = 4\pi \times 10^{-7}$ Tm/A.)

(a): What is the total number of turns in the coil?
(b): How many joules of energy are stored in the coil at t = 0?
(c): How long does it take for the stored energy to fall to half its initial value?
(d): What is the power dissipated in the resistance 1 ms after the battery is switched off?

5.

GENERATOR: [11 marks, 4 for a) & c), and 3 for b)] Some energetic students are ``flipping" a large circular coil (radius r = 5 m, N = 1000 turns) about an axis perpendicular to the Earth's magnetic field in Vancouver. The maximum B field through the coil is $0.3 \times 10^{-4}$ T. If the students crank furiously but smoothly at a steady rate of 2 rotations per second, find:

(a): the maximum current that flows from this generator through the 100 $\Omega$ resistance of its own wires, if we connect the ends of the coil together;
(b): the average power dissipated in said 100 $\Omega$ resistance;
(c): the diameter of the copper wire (circular cross section) from which the coil is wound. (The resistivity of copper is $1.7 \times 10^{-8} \Omega$ m.)

6.

DAMPED OSCILLATIONS: [10 marks, 2 for a), and 4 each for b) & c)] We have an RLC series circuit, as shown, with $R=10 \;\Omega$ , L=10^-4 H, C=10^-6 F.

(a): Write down the circuit equation which gives the voltage drops around the entire circuit.
(b): If we start with a charged capacitor how long does it take for the amplitude of the oscillating current to fall to half of its original value?
(c): What is the frequency of the charge oscillations?

Sorry, Figure unavailable!

7.

THIN FILM INTERFERENCE: [15 marks, 5 for a), and 10 for b)] You have a circular glass lens (cut from a sphere of radius 21.2 m) resting on top of a piece of perfectly flat glass. Viewing the lens with green light of wavelength 525 nm, incident normally from above, you see alternate bright and dark circular bands which are closer and closer together as their distance from the point of contact increases.

(a): Do you see a dark or bright circle at the centre (point of contact)? Explain why.
(b): Viewed from the top, what is the radius of the 17 $^{\rm th}$ dark circular band?

Sorry, Figure unavailable!

8.

DIFFRACTION: [16 marks, 4 for each part] We have a system of 5 slits with a separation between the centres of adjacent slits of $6.0 \times 10^{-6}$ m and a slit width of $2.0 \times 10^{-6}$ m, illuminated with light of wavelength $5.0 \times 10^{-7}$ m.

(a): What are the angles (in radians) relative to the central axis (m = 0) at which principle maxima of order m = 1 and m = 2 occur?
(b): What is the ratio of the light intensity for the principal maxima of order m = 1 & 2 compared to that for m = 0?
(c): Give a phasor diagram showing the resultant for the light amplitude at an angle halfway between the m = 0 and m = 1 principal maxima.
(d): Using the graph below make a drawing, as quantitative as you can, for the light intensity for all angles between the m = -2 and m = +2 principle maxima. Indicate the angular units, in radians, of the abscissa and the light intensity units in terms of I₀, the intensity from a single slit by itself.

9.

PROBABILITY: [19 marks, 10 for a), and 9 for b)]

(a): In a normal full deck of playing cards there are 52 cards, all different, with 13 cards (2,3,4,5,6,7,8,9,10,J,Q,K,A) in four different suits ( $\clubsuit$ , $\diamondsuit$ , $\heartsuit$ , and $\spadesuit$ ). What is the probability that when you pull 7 cards at random from the deck, without replacing any card, you have a ``Royal Flush"? Having a ``Royal Flush" means that your 7 cards include A,K,Q,J & 10, all of the same suit, plus any two other cards.
(b): You have a bucket full of buttons (thousands and thousands of them) all identical except for colour. There are many different colours. You take out a cupful (containing very many buttons) and spill them on a table, counting only the red buttons. You repeat this many times, each time returning to the pail the buttons spilled on the previous trial and mixing the buttons in the pail well. After many such trials you notice that a cupful contains, on average, 6 red buttons. What is the probability that the next cup will contain three or less red buttons?

Jess H. Brewer
1999-02-25