29:28 Physics II
Spring 2006
Third and Last Hour Exam ...May 10, 2006

Write legibly. Start each question on a new page. It allows me to make comments and generally keeps me in a better mood. Clearly describe what you are trying to do; it can help for partial credit. There are 5 questions. Notice the table of fundamental constants attached to the exam. Ask questions if you think a question (or questions) is written in a confusing fashion.

Walk with Ursus!!!

Note: The following questions cover only the last third of the course. The real thing on Wednesday will have 5 questions over the last third of the course, and five more over the entire semester.

1. A circular loop of radius $R$ carries a current $I$, which flows in counterclockwise fashion. A magnetic field of magnitude $B$ is inclined to the normal of the plane of the loop at an angle $\theta < \pi/2$. Describe how the loop responds. Use equations and technical terms.

2. Describe in two or three legible sentences what happens when a paramagnetic substance is placed in an external magnetic field. Does the paramagnetic substance make the total field (external + that of sample) larger or smaller than the external field by itself?

3. A solenoid has a radius $a$, a length $L \gg a$, and $n$ turns of wire per meter. The current flowing through the solenoid depends on time as:
   $-\infty < t < 0: I=I_0$
   $0 < t < \tau: I=I_0 + bt$
   $\tau < t < +\infty: I=I_0 + b\tau$
   where $I_0$ is a constant. What is the EMF as a function of time? Does it enhance or impede the flow of current through the solenoid?

4. A circuit contains an inductor and resistor in series with a power supply. The power supply is initially off, then turned on. Derive, or write down the equation for the current in the circuit, and make an accurate sketch of the current as a function of time, with clearly labeled axes.

5. A $\sf U$-shaped tube is open to the atmosphere on one side (let's say the right side), and connected to a pressure $p_0 > p_{atm}$ on the left side. There is a liquid with density $\rho$ much greater than that of air in the tube. Describe the level of the liquid in both sides of the tube. Use equations.

6. A large tank has a base with dimensions $l$ and $w$, and is filled with water to a depth $h$. A ship with mass $M$ is placed in the tank. How much does the level of the water change, and does it rise or drop?