Physics 114 –Summer 2007

Participation Points #4

To be turned in at the end each discussion session, stapled on top of #3, #2 & #1

Use provided space to show your work only, use back page for notes

-TA (HW grading, tutoring, solution manual,…) information: Praveen Nittala (Praveen.nittala@umb.edu), S-3-013

-Tutoring schedule (in room S-3-013): 10:00 -5:30 (Mondays to Thursdays)

Student’s Name:____________________ Team #________ Prev. points

1.- (a) Can an induced electric field exist in the absence of a conductor? Write an expression of Faraday’s Law to support your answer

(b) Draw the similarities between the magnetic field created by a sheet of current density J of thickness h pointing out from the page, and the electric field created by an infinite region (of thickness h) of a time varying magnetic field pointing into the page, using Ampere’s Law and Faraday’s Law, respectively, and state what quantity play the role of the source of the magnetic and electric fields, respectively, in each case.

(c) A constant uniform magnetic field points into the page. A flexible, circular conducting ring lies in the plane of the page. If the ring is stretched, maintaining its circular shape, what’s the direction of the induced current? Explain why.

2.- A circular wire loop of resistance R and radius a lies with its plane perpendicular to a uniform magnetic field. The field strength changes from an initial value B₁ to a final value B₂. Show, by integrating the loop current over time, that the total charge that moves around the ring is . Note that this result is independent of how the field changes with time.

3.- (a) When two coils are connected in series but are physically far apart, they behave as a single inductor whose inductance is the sum of individual inductances. Why this might not be true if they are closer together?

(b) List two similarities and two differences between inductors and capacitors.

4. Mutual inductance. A rectangular loop of length l and width w is located a distance a from a long, straight, wire, as. What is the mutual inductance of this arrangement?

5.- Self-inductance. What is the self-inductance of a solenoid 50 cm long and 4.0 cm in diameter that contains 1,000 turns of wire?

6.- Inductors. The current in a 2.0-H inductor is decreased linearly from 5.0 A to zero over 10 ms. (a) What is the average rate at which energy is being extracted from the inductor during this time?

(b) Is the instantaneous rate constant?

7.- (a) Unpolarized light is incident on two sheets of Polaroid with their polarization directions at right angles, no light gets through. A third sheet is inserted between the other two, now some lights get through. How can this be?

(b) The intensity of light falls off as the inverse square of the distance from the source. Does this mean that the electromagnetic (EM) wave energy is lost? Explain.

8.- EM waves. (a) Your intercontinental telephone call is carried by electromagnetic waves routed via a satellite in geosynchronous orbit at an altitude of 36000 km. Approximately how long does it take before your voice is heard at the other end?

(b) What are the wavelengths of (i) a 100-MHz FM radio wave,

(ii) a 3.0-GHz radar wave,

(iii) a 6 x 10¹⁴ Hz light wave

(iv) a 1x10¹⁸ Hz x- ray?

9.- Wave momentum & Radiation pressure. A laser beam shines vertically upward. What laser power is necessary for this beam to support a flat piece of aluminum foil with mass 30 micro gram and diameter equal to that of the beam? Assume the foil reflects all the light.