1. (25) Three point particles are arranged along the axes of a Cartesian coordinate system. Each charge is a distance 0.5 m from the origin. The top particle lies along the positive y-axis and has a charge of +3 C while the other two particles lie along the positive and negative x-axis and each have a charge -4 C.
2. (30) Consider a very long, cylindrical rod of radius a and length L that contains a uniformly distributed charge +3Q (a cross-sectional view is shown to the right). A gap exists in the region a < r < b, and a coaxial cylindrical conducting shell, also of length L, occupies the region b < r < c. A total charge of +Q is placed on the conducting shell, distributing itself appropriately. Ignore edge effects when answering the following questions; that is, assume L >> c and, for parts b and c, consider only regions roughly near the center of these long cylinders.
a.. How much charge resides on the outer surface of the conducting shell, at r = c?
b. What is the electric field as a function of distance, r, in regions I, II, III?
c. What is the electrical potential V on the outer surface of the conducting cylinder, assuming that V = 0 at the center of the inner cylinder, r =0.
3. (30) A 9 V battery can be connected through a 1000 ohm resistor and a switch to a parallel combination of a resistor, R = 1000 ohms , a capacitor, C = 300 mF, and an inductor, L = 500 mH. The switch has been open for a very long time.
A. Just after the switch is closed, find the voltage across and current through each of the three circuit elements, R, C and L.
B. A long time after the switch is closed, find the voltage across and current through each of the three circuit elements, R, C and L.
C. The switch is left closed for a long time and then is reopened. Find the current through each of the three circuit elements, R, C and L just after this is done. (You don't have to provide the voltages.)
4. (20) A long straight but hollow wire carries a current I uniformly distributed throughout its area (excluding the hollow). The inner radius of the wire is ri while the outer radius is ro. Find the magnitude of the magnetic field as a function of distance from the axis of the wire.
5. (20) A long solenoid or radius R1 = 5 cm has n = 100 turns per cm. Centered within this solenoid is a 10 turn coil of radius R2 = 2.5 cm. A current of 10 A flowing through the outer solenoid is reduced to zero uniformly over a time of 5 seconds.
A. What is the magnitude of the EMF that appears across the inner coil as the current is being reduced?
B. If, looking down along the axis of this system, the original current had been flowing counterclockwise, in what direction is the EMF in the inner coil. EXPLAIN your reasoning; a 50/50 guess at the right answer is worth no credit!
6. (10) A cylindrical resistor of length L = 2 cm is constructed from an inner cylindrical core of radius R1 = 3.0 mm, made from material of resistivity r1 = 1.5 ohm-cm and an outer shell, which has an inner radius equal to R1 and an outer radius R2 = 4 mm, made from material of resistivity r2 = 3.0 ohm-cm. What is the total resistance of this device?
7.(25) An electromagnetic wave traveling in vacuum is
described by the formula
with E in V/m, y in m
and t in secs. Its wavelength l
is 550 nm.
A. What is the value of k?
B. What is the frequency f of this wave?
C. What kind of radiation is this: visible light, infrared, radio, x-ray, uv, etc.?
D. In what direction is this wave traveling?
E. What is the direction of polarization of this wave?
F. Write an expression, in the form given for E, for the magnetic field component of this traveling wave.
8. (10) If the pupil of your eye can open as much as 5 mm, in diameter, what is the smallest distance you can resolve on a piece of paper 30 cm away, using light with a wavelength of 550 nm?