Physics 212 – Final Exam NAME:______________________

Summer 2003 STUDENT ID#:_______________

Friday, 15 August 1110 - 1310

Prof. Milos Steinhart

INSTRUCTIONS: This is a closed book exam. Calculators are allowed. You must show all of your work in the space provided for each question and you must include appropriate units and significant figures. If you need more space, use the other side of the paper but mark clearly to which problem and which question is your work related. Try to make your work as clear and transparent as you can. Even if you understand the problem well, think twice, what you are precisely asked.

Do not use other papers!

You are bound by the University’s Honor Code. Any evidence of cheating must be reported to the College of Arts and Sciences.

PLEASE CIRCLE ALL ANSWERS

All problems are worth 20 points.

SCORE

Problem 1 _____________________

Problem 2 _____________________

Problem 3 _____________________

Problem 4 _____________________

Problem 5 _____________________

TOTAL _____________________

Problem 1: A solid nonconducting sphere of radius r₀ has a total charge Q. The charge density is directly proportional to the radius, so: r_e(r) = b r. Calculate

a) (6) the exact behavior of the charge density in terms of Q:

b) (6) the electric field at points inside the sphere (r < r₀):

c) (4) the electric field at points on the sphere (r = r₀):

d) (4) the electric field at points outside the sphere (r > r₀):

Problem 2: Suppose you are looking at two current loops in the plane of the page as shown in the figure. When the left circuit is closed at some instant by the switch:

(To get any credit here, mark clearly all the directions and explain your choice!)

a) (4) what is the direction of induced current in the right loop?

b) (4) does the situation change after some time?

c) (4) what is the direction of the induced current in the right loop if it is pulled to the right?

d) (4) what happens if we rotate the right loop in the plane around the left one at a constant distance?

e) (4) what happens when we open the left circuit?

Problem 3: Our favorite local radio station broadcasts on a carrier frequency 1040 kHz. If we find at home a coil with the inductance L = 4 mH,

a) (4) what capacitance do we need to build a simple one-circuit radio?

b) (4) Make drawing of the (main parts) of the tuning circuit?

c) (4) How long would the l/2 dipole antenna be?

d) (4) If we listen for 8 minutes, how many waves will pass the antenna during this time?

e) (4) How far will the first wave get by then?

f) (optional +5 points) Compare the distance from e) to some distance important in Nature.

Problem 4: An aquarium filled with water (n_w = 1.33) has flat glass sides whose index of refraction is n_g = 1.58. A beam of light from outside (air) the aquarium strikes it at a 43.5° angle of incidence. What is the angle of this light when it

a) (5) enters the glass?

b) (5) when it after enters the water?

c) (5) What would be the angle if the same beam entered water directly from air?

d) (5) Make some physically reasonable conclusion from b) and c) considering also the conditions of validity of your statement.

Problem 5: Multiple choice. Pick the single best answer or answers to each conceptual question below. Please include a brief explanation for partial credit. Each answer is worth of 4 credits.

1. A capacitor is connected to a tunable oscillating power source. As the frequency of the power source increases, the impedance or capacitive reactance

a) increases.

b) decreases.

c) remains the same.

d) depends on the direction of the current.

2. In planar harmonic electromagnetic wave, the magnetic field achieves its maximum when the electric field

a) is also at its maximum.

b) is at zero.

c) is at its minimum.

d) is at some intermediate value.

3. Which is (are) true? The energy carried by an electromagnetic wave in a vacuum

a) propagates at the speed of the light.

b) consists of equal contributions from the electric and magnetic fields.

c) propagates along the direction of the electric field.

d) all of the above.

4. The phenomenon of dispersion occurs when

a) there is total internal reflection.

b) the index of refraction depends on the wavelength.

c) there is a virtual image.

d) the incident beam is completely reflected.

5. For a thin lens made of two spherical surfaces, the focal length depends on

a) the index of refraction of the lens.

b) the radii of the two spherical surfaces.

c) the assumption of the incident rays near the optical axis.

d) the lateral size of the lens.