EXAM 3 May 13, 1998 PHYS 208

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No notes, books, etc. may be used during this exam.

g = 9.8 m/sec^{2} |
Radius of the earth = 6.38 x 10^{6} m |

The mass of the electron is 9.11 x 10^{ -31} kg. |
e = 1.60 x 10 ^{ -19} C |

1 -------------- = 9.0 x 10 |
mu |

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

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 = ------- BWhat changes if you reverse the direction of the magnetic field? Why?^{2}w^{2}