This test is 90 minutes long and has a total of 100 points.
[15 points] 1. Multiple choice questions. Each question is worth 3 points. Partial credit may be given for an incorrect answer if work is shown.
(i). A uniform magnetic field B = 0.50 T is directed perpendicular to the plane of a circular loop of wire of radius 0.25 m. The magnetic flux through the loop is:
[ ] zero
[ ] 0.031 T m2
[ ] 0.098 T m2
[ ] 2.55 T m2
(ii). A generator of AC electricity contains a coil with 25 turns (i.e., N = 25) in a uniform magnetic field of strength B = 0.33 T. The coil has an area of 0.50 m2, and is spinning at a frequency f = 60 Hz. The axis of rotation of the coil is perpendicular to the magnetic field (this is the standard arrangement). What is the peak voltage generated by this generator?
[ ] 248 V
[ ] 350 V
[ ] 1555 V
[ ] 2200 V
(iii) The average distance between the Earth and the Sun is 1.49 x 1011 m. How much time, in minutes, does it take for light to travel from the Sun to the Earth?
[ ] zero
[ ] 2.01 x 10-3 minutes
[ ] 0.138 minutes
[ ] 8.28 minutes
[ ] 497 minutes
(iv). An astronomer observes that electromagnetic waves emitted by oxygen atoms in a distant galaxy have a frequency of 5.710 x 1014 Hz. In a lab on Earth, oxygen atoms emit waves with a frequency of 5.841 x 1014 Hz. Determine the relative velocity of the galaxy with respect to the Earth.
[ ] 6.73 x 106 m/s, away from the Earth.
[ ] 6.73 x 106 m/s, toward the Earth.
[ ] 4.37 x 106 m/s, away from the Earth.
[ ] 4.37 x 106 m/s, toward from the Earth.
[ ] 3.36 x 106 m/s, away from the Earth.
[ ] 3.36 x 106 m/s, toward from the Earth.
(v). Unpolarized light with an intensity of 400 W / m2 is incident on a polarizer; the polarization axis of the polarizer is at 20° to the vertical. What is the intensity of the transmitted light?
[20 points] 2. Induction.
A conducting rod of length L = 0.10 m lies on a pair of conducting rails in a region where a uniform magnetic field of 2.0 T is directed into the plane of the paper, as shown. The battery has an emf of 6 V, and the resistor has a resistance of R = 0.3 ohms. (Everything else has negligible resistance.)
[4 points] (a) The rod is initially clamped in place so that it can not move. What is the current in the rod?
[4 points] (b) The rod is now unclamped so it is free to move without friction on the rails. In which direction will it move? Justify your answer.
[6 points] (c) As the rod moves, a motional emf is developed in it. Does this motional emf cause the current in the loop to increase, decrease or does the current stay the same? Justify your answer.
[6 points] (d) The rod is eventually observed to be moving with a constant velocity. What is this velocity? State both the magnitude and the direction. [Hint: what is the net force on the rod?]
[20 points] 3. AC Circuits
A light bulb has a resistance of 240 ohms. It is connected to a standard wall socket (in North America a wall socket has Vrms = 110 V, f = 60.0 Hz).
[3 points] (a) Determine the rms current in the bulb.
[3 points] (b) How much power is dissipated in the bulb?
[6 points] (c) Determine the value of the inductance, L.
[4 points] (d) What is the rms current in the RLC circuit?
[4 points] (e) It is possible to connect the bulb to a 220 V wall socket (the European system) using only a transformer so that the power dissipated in the bulb is the same as that in part (a). Explain in detail how you would do this, suggesting possible values for the number of turns in the primary and secondary.
[10 points] 4. Parallel rays.
Three parallel rays are incident on a converging lens; the lens has a focal length of 3.0 cm. In each of the two cases below, draw the path of each light ray and state the x and y coordinates of the point where the rays converge.
Assume the lens lies at the origin of an x-y coordinate system, and the grid has a spacing of 1 cm by 1 cm.
[5 points] (a) The rays are parallel to the principal axis, and shine on the upper half of the lens.
The rays converge at: x = ______ cm y = ______ cm
[5 points] (b) The rays are parallel to the principal axis; a plane mirror is placed at x = 2 cm, parallel to the y-axis.
The rays converge at: x = ______ cm y = ______ cm
[15 points] 5. Refraction
A light source lies at the bottom of a pool of water. It emits a beam of light that strikes the interface between the water and an unknown medium at 45°. The index of refraction of water is n = 1.33.
[5 points] (a) If the refracted beam passes through point A (x = 1, y = 2), what is the index of refraction of the unknown medium?
[5 points] (b) If, instead, the refracted beam passes through point B (x = 2, y = 2), what is the speed of light in the unknown medium?
[5 points] (c) What would the index of refraction of the unknown medium have to be for all the light to be totally internally reflected so it passed through point C? Is this possible? Justify your answer.
[20 points] 6. A lens
A certain lens produces a real, inverted image of a particular object. The image is 30 cm away from the object, and is exactly half as large as the object.
[3 points] (a) What kind of lens produces this image?
[6 points] (b) How far from the object is the lens placed? Hint : use the magnification equation, m = -di / do, and one other condition to determine di and do, or look at one of the principal rays.
[5 points] (c) What is the focal length of the lens?
[6 points] (d) Draw a ray diagram on the diagram above to show how the image is produced by the lens. (Hint : draw in the lens first.)