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EXAM 3                       May 8, 1996                          PHYS 208

Name:________________________________________________________

Write a 6-10 letter code here if you would like me to post your
final grade on the web page.

______________________
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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 e = 1.6 x 10-19 C 1 / (4 pi epsilon0 ) = 9.0 x 109 N m2 / C2 The mass of the electron is 9.11 x 10-31 kg.

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).

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For the remaining problems, place the equations representing the physics principles you are using in the box on the page. You may use an English label for the principle, the general form of the equation, or the form you get applying the principle to the problem at hand.

2. (30 points)

Show carefully that the field between two wires a distance d apart, carrying current in opposite directions is

```
mu  I
0             1             1
B = ------- [   ---------- + -----------  ]
2 pi       d/2 + x       d/2 - x

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Diagram:

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3. (30 points) (From homework)

A resistor R and an inductor L are connected in parallel across an AC generator. The source EMF is E = E0 cos (omega t). Determine the current through the resistor and the inductor (including amplitude and phase) as a function of time. What is the total current leaving the source (you need not make Itot algebraically pretty; any correct expression is acceptable).

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Diagram:

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4. (30 points)

Show that the inductance per unit length of the wires in problem 2 is

L/l = ( mu0 / pi ) ln [ (d - a) / a ]

where a is the radius of the wire. [The voltage across an inductor is - L dI/dt ].

Neglect the flux within the wires.

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Diagram:

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