Physics 122 Final Exam - 18 April 1996

1.

``QUICKIES''   [16 marks - 2 each]

(a)

The six quarks which can be combined into composite particles are, in alphabetical order:  bottom, charmed, down, strange, top, up.  [Underline the one which is the heaviest.]

(b)

The four fundamental forces of nature are, in alphabetical order:  electromagnetism, gravity, strong, weak.  [Underline the one governing beta decay.]

(c)

In the same room we have a mixture of helium gas, oxygen gas, etc. What is the ratio of the helium average velocity to that of the oxygen molecules?

(d)

If I have a town which averages 3 motorcycle fatalities per year, what is the probability that in a given year none occur?

(e)

If I have an inductance of $3 \times 10^{-6}$ H and a capacitance of $3 \times 10^{-6}$ F, the frequency of oscillation of the two elements combined in a circuit is                             Hz.

(f)

If I have glass (index of refraction 1.40) what is the minimum thickness of plastic (inside of refraction 1.30) such that light of wavelength $545 \times 10^{-9}~m$ has minimum reflection?                             m.

(g)

I have a diffraction grating which has 23,000 lines per cm and has a width of 4 cm. Fully illuminated, what is its resolving power in third order?

(h)

I have crossed magnetic and electric fields and I observe that protons of velocity $4.0 \times 10^6$ m/s, perpendicular to both fields, pass through the system undeflected. If the electric field strength is 35,000 V/m, the magnetic field strength must be                             T.

2.

Electromagnetic Force   [15 marks] At t = 0 an electron ( $q = -1.602 \times 10^{-19}$ C, $m = 9.11 \times 10^{-31}$ kg) is at position (x, y, z) = (0,0,0) and moving with velocity $3.0 \times 10^6$ m/s along the positive x-axis, in a region of space where the electric field (33 V/m) and the magnetic field ( $1.30 \times 10^{-5}$ T) are both uniform and pointing along the positive z-axis.

(a)

[8 marks]   What is the speed of the electron at $t = 1.2 \times 10^{-6}$ s?

(b)

[7 marks]   What is the position of the electron (x, y and z-coordinates) at $t = 1.2 \times 10^{-6}$ s?

3.

Resistance:   [10 marks] We have seven equal resistances (R = 120 $\Omega$) connected as shown to a battery ($\epsilon$ = 12 V). How much current flows out of the battery?

Figure not available, sorry!

4.

LC Circuit Time-Dependence:   [12 marks] In an LC circuit with $C = 90~\mu$F, the current is given as a function of time by i = 3.4 cos (1800 t + 1.25), where t is in seconds and i is in amperes.

(a)

[4 marks] How soon after t = 0 will the current reach its maximum value?

(b)

[4 marks] Calculate the inductance.

(c)

[4 marks] Find the total energy in the circuit.

5.

A.C. Circuit:   [10 marks] We have an oscillator ( $V = V_m sin \omega t$, with V_m = 120 V and frequency = 60 cycles/sec.) connected in series to a resistance ( $R = 30 \; \Omega$) an inductance (L = 0.050 H) and a capacitance ( $C = 65 \; \mu$F).

(a)

[6 marks] What is the maximum current in the circuit?

(b)

[4 marks] What is the average power delivered to the circuit?

6.

Thin Film Interference:   [10 marks]

We have a very thin oil film (index of refraction = 1.25) on water (index of refraction 1.33) on which sunlight is incident perpendicularly. At the edge of the film the thickness is zero and the thickness grows linearly toward the centre. As we proceed from zero thickness we first see a violet color band (wavelength 430 nm) and then all the colors of the rainbow until we see violet again.

(a)

[6 marks] What is the thickness of the film at the first violet band?

(b)

[4 marks] What is the thickness of the film at the second violet band?

Explain your answers.

7.

Resolving Images:   [10 marks]

We have a circular radio telescope of diameter 95 m receiving radiowaves from the sun (earth-sun distance = $1.50 \times 10^{11}$ m) of wavelength 21 cm. What is the minimum separation distance of two sources on the sun which can be resolved by the telescope?

8.

Multiple Slits:   [18 marks]

We have 5 narrow and equal slits, each separated from its neighboring slit by the same spacing (0.025 mm). We illuminate the slits coherently with light of wavelength 500 nm. On a distant screen (distance from slits = 5.00 m) we observe the 5-slit diffraction pattern. The slits are so narrow that single-slit diffraction does not affect the pattern. [Use the back of the last page if you need more room for your answers.]

(a)

[3 marks] Draw, qualitatively, the diffraction pattern seen on the screen showing the central maximum and one principal maximum on either side, as well as the little maxima in between.

(b)

[3 marks] Label, in mm, the distance on the screen from the central maximum to each of the zeros of intensity.

(c)

[4 marks] Draw four phasor diagrams, as follows:

i)

for the central maximum;

ii)

for the first zero beyond the central maximum;

iii)

for the second zero beyond the central maximum;

iv)

for the middle ``bump" in between the principal maxima.

(d)

[3 marks] What is the ratio of the light intensity at the principal maxima to that half way in between?

(e)

[4 marks] If the slits were of finite width ( $5.00 \times 10^{-6}$ m) what would be the ratio of intensity of the central maximum to that of the first principal maximum on either side?

9.

Probability:   [19 marks]

(a)

[8 marks] Two Physics 122 students, A & B, are tested with a series of questions which are marked right or wrong (no part marks). Student A averages 80% right and student B 60%. I bet you my $1 to your $8 that on the next 4 questions, chosen at random, B will get more right answers than A. Is this a smart bet for me? Analyze the probabilities of the various outcomes for both A & B to justify your answer.

(b)

[8 marks] You are dealt 13 cards at random from a full deck of 52. What is the probability that 11 of your 13 cards will be red (that is, belong to the two red suits, hearts and diamonds, rather than to the two black suits, clubs and spades)?

(c)

[3 marks] (More challenging but for fewer marks.) What is the probability that your 13 cards in a random deal are exactly 6 hearts, 5 diamonds, 1 club and 1 spade? [Hint:  Remember the deal of part (b).]