29:28 Physics II
Spring 2005
Second Hour Exam ...April 1, 2005

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 6 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. Work hard: don't live up to today's name!

Walk with Ursus!!!

(1) A $50 \mu F$ capacitor is charged up to 12 V.
(a) What is the charge stored on each plate of the capacitor?
(b) The capacitor is disconnected from the power supply and discharges through a circuit that limits the current to $10^{-6}$ A. How long does it take for the capacitor to fully discharge?

(2) A portion of a circuit is shown in Figure 1. To the right of resistor A, there are other circuit elements. The total current going through the power supply is

$$I =\frac{V(R_A + R_B)}{R_A R_B}$$ (1)

What can you say about the circuit to the right of resistor A? You should be able to not only say what sort of circuit components are out there, but also the values of those components.

Figure:

(3) Two oxygen nuclei, one of the isotope $^{16}O$ and the other the heavier isotope $^{18}O$ have a velocity $\vec{v} = 1.0 \times 10^7 \hat{e}_x$ m/sec. They enter a region with a magnetic field as shown in Figure 2. The magnetic field has a strength of 0.10 T. At what distance from the opening will each of the nuclei impact the wall?

Figure: Oxygen isotopes in a magnetic field

(4) In Figure 3 below, a plane contour is shown in a region containing electrical currents. The numbers indicate the magnitudes of those currents. What is the value of $\oint \vec{B} \cdot \vec{ds}$ where the direction of the path (i.e. direction of increasing $\vec{ds}$) is indicated. Write a sentence or two describing how you got your answer.

Figure:

(5) A wire is formed into an equilateral triangle with side $a$. A current $I$ flows in this equilateral triangle. What is the vector magnetic field at the center of the equilateral triangle. The center of an equilateral triangle is defined as the point at which the perpendicular bisectors of each of the three sides intersect.

(6) A voltage is made at the terminals of a coil by rapidly rotating the coil in a magnetic field. The strength of the magnetic field is 0.050 T. The coil consists of 100 loops of wire in a circle with radius of 10cm. The loop is rotated at a rate of 4 cycles per second (0.25 sec rotational period). What is the voltage that appears at the terminals of the coil?