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EXAM 3                         May 13, 1998                           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 The mass of the electron is 9.11 x 10 -31 kg. e = 1.60 x 10 -19 C ``` 1 -------------- = 9.0 x 109 N m2/C2 4 pi epsilon0 ``` ```mu0 ---- = 1 x 10-7 Henry/m 4 pi ```

1. (10 points) Quote Gauss's, Ampere's, and Faraday's laws, and explain how you can use the similarities among them to help remember the forms. Which law plays for the calculation of magnetic fields a role equivalent to that played by Gauss's Law for the calculation of electric fields. [You needn't know which name goes with which law.]

2. (30 points) (Modified from homework) Find the magnitude of the effective impedance for a resistor R in series with a parallel combination of an inductor L and a capacitor C.

3. (30 points) A solenoid has length x, N turns, and a circular cross-section of radius R, where R<<x. Find a relation for the magnetic field inside the solenoid and use this relation to show that the inductance of the solenoid is

L = mu0 pi R2 N2 / x

4. (30 points) In the accompanying figure, a horizontal wire of length w and resistance R slides freely on the vertical members of a U-shaped conductor of negligible resistance. There is a uniform horizontal magnetic field of magnitude B over the entire region. A mass m is attached to the slide wire, whose own mass is negligible. Show that the mass descends with a terminal speed of

```
R m g
v = -------
B2 w2
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What changes if you reverse the direction of the magnetic field? Why?