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EXAM 3                         May 14, 1997                          PHYS 208
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Name:________________________________________________________

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If you need a constant not given here or do not understand a problem, please ask me about it.
No notes, books, etc. may be used during this exam.

 g = 9.8 m/sec2 Radius of the earth = 6.38 x 106 m Mass of the electron = 9.11 x 10-31 kg. e = 1.60 x 10-19 C ```mu0 ---- = 1 x 10-7 Henry/m 4 pi ``` ``` 1 -------------- = 9.0 x 109 N m2/C2 4 pi epsilon0 ```
For all problems, place the equations representing the physics principles you are using in the box on the page. You may use the general form of the equation or the form you get applying the principle to the problem at hand. If no diagram is applicable to a problem, write "none" in the diagram section.

1. (10 points)
(a) Give a good, quick way of remembering the Biot-Savart law for the magnetic field due to a infinitesimal segment of current.       (b). Name the magnetic-field equivalent of Gauss's Law for electric fields and explain the analogies between the two. 2. (30 points, from homework) The circuit shown in the figure is called an RC high-pass filter because high input frequencies are transmitted with greater amplitude than low input frequencies. If the input voltage is

Vin = V0 cos(omega t),

find the amplitude of the output voltage.

Diagram:

Principles:
3. (30 points) A metal ring of area A is placed in a constant, uniform field B in such a way that its area vector makes an angle theta to the lines of B. The loop now rotates about a diameter so that theta = omega*t. If the resistance of the coil is R, find the current through the coil as a function of time.

Diagram:

Principles:
4. (30 points) A very long, straight metal tube has inner radius a and outer radius b . A current whose density is J = cr flows down the tube. Find the magnetic field in the empty region inside r = a and also within the metal, a < r < b .

Diagram: Principles:

Use this page if necessary to continue any of the problems. Be sure to label the problem number.