Q1) A circular wire of radius a carries current in the z^. The current density is J→ = J0z^ everywhere except in a circular hole radius a/2 which runs the length of the wire and is centered a distance a/2 away from the center axis of the wire. What is the magnetic field inside the hollow region?
Q2) Find the total power delivered to the following circuit:
Q3) A two terminal "Black Box" is known to contain one lossless inductor, L, one lossless capacitor, C, and a resistor, R. When a 1.5V DC battery is connected, a current of 1.5mA flows. When an AC voltage of VRMS = 1.0V @60Hz is connected, a current of IRMS = 10mA flows. As the frequency is increase (while the applied voltage is held constant) the current is found to go through a maximum exceeding 100A at f = 1kHz.
a. What is the circuit inside to box?
b. What are the values of R, L, and C?
Q4) On an Optical bench, an |f1| = 1m convex lens sits at the zero mark. An |f2| = 2m concave lens is placed at the 10m, and an |f3| = 5m concave mirror sits at the 20m mark. If you were to place an object at the 5m mark and look through lens 1:
a. How many images would you see?
b. What is the apparent location, orientation, and magnification of each image?
Q5) A Resistor, R is connected in series to a capacitor, C, an inductor, L, a switch, S, and a battery supplying an EMF, ε. At time, t = 0, the switch is closed, and current begins to flow.
a. At what value of R (as a function of L and C) does the system behavior change?
b. There are three regimes in which this system operates (underdamped, overdamped, and critically damped). Find the current as a function of time, I(t), for each case.
c. In the underdamped case, how long will it take the current to reach half its initial value?
