Recitation section number (or day/time):___________________________

This is a closed book exam; the formula sheets provided are the only supplemental material permitted on this exam.

Programmable calculators and graphing calculators may be used during this exam, but not for storage of additional notes or formulas.

Show ALL work on problem sheet and only on that sheet.

Please read questions carefully.

Credit may be lost inadvertently if solutions are not neat and orderly.

Be careful with units, signs, and significant figures.

1. (25 points)

Briefly justify all answers.

1. What is the brightness of the lamps relative to each other in the circuit at the right?

2. When lamp C is disconnected, how does the brightness of the remaining two bulbs change relative to part a?

3. The driving frequency applied to a certain RLC series circuit is greater than the circuit's resonant frequency. Does the emf lead or lag the current?

4. We have uncovered five facts regarding the electrostatics of a charged conductor. Which two are derived from Gauss's law?

5. Two conducting loops with a common axis are placed near each other as shown. Initially the currents in both loops are zero. Suddenly a current i_a is set up in loop a, with direction as shown (counterclockwise looking down the axis).
   • In which direction in the current induced in loop b?
   • Is the force between the loops repulsive or attractive?

6. Consider a velocity selector that consists of perpendicular, uniform electric and magnetic fields, with the B field directed straight up. A beam of positively charged particles passing through the velocity selector from left to right is undeflected by the fields (F_mag equal and oppositely-directed to F_el).
   • Is the electric field into or out of the page?
   • The direction of the particle beam is now reversed to that it travels from right to left. Is the beam deflected now? If so, in which direction?

Indicate the equation number most relevant to each phenomenon listed in the table.

1	2	3	4	Electromagnetic Phenomenon
				Coulomb's law.
				The displacement current.
				Under static conditions, excess charge resides on the surface of a conductor.
				The magnetic field is not a conservative field.
				A changing magnetic field generates an electric field.
				A changing electric field generates a magnetic field.
				Electric charge is accompanied by an electric field.
				Electric current is accompanied by a magnetic field.
				There are no magnetic monopoles.
				Electromagnetic waves propagate at the speed of light. (Pick two!)

Finally the semester is over and you are ready to go on a camping trip. Eager to check the condition of a lantern battery left over from last summer, you grab a multimeter and two test resistors and make the following measurements. When R = 10 ohm, the current in the circuit is 0.50 A. When R = 5 ohm, the current in the circuit is 0.88 A. What is the battery's emf and internal resistance?

Arriving late at the campsite (because the PHYS208 final exam was on the last possible day!), you discover that the only remaining campsite is at the entrance to the park. An annoying flashing yellow light has been placed a few feet away to alert other campers of a nearby pothole. The lamp is flashing every two seconds and is making it difficult to sleep. Investigating, you find that the lamp circuit is as shown in the figure. The battery pack is labeled 60 V; the capacitor is labeled 1.0 microF. Unfortunately the resistor is unlabeled. You recall that one of the 1992 PHYS208 midterm exams considered such a circuit:

The flashing lights seen on barricades at street work and construction sites are driven by a relaxation oscillator circuit as shown in the figure, with N being a neon lamp. The lamp is nonconducting until the voltage across it (And the capacitor also) rises to a value of 45 V whereupon it "ignites," dropping its resistance almost instantly to zero and discharging the capacitor. Then the lamp again becomes nonconducting and the process repeats.

How many ohms of resistance should be added in parallel to the existing resistor to make the flashing occur faster than the eye can distinguish (25 flashes per second; that is, 0.04 second between flashes)?

When you return from your camping trip, you discover that your cousin has won the Powerball lottery. The entire family is headed to France to celebrate. You reluctantly agree to accompany them - you had been looking forward to finally completing the work on the custom motor you had designed for the 1998 Punkin’ Chunkin’ contest. Begrudgingly you throw the motor parts into a bag and head for the airport.

Your motor is wound with an inductance of 16 mH and a resistance of 3.0 ohm. It has been optimized for the largest possible operating current at 60 Hz by adding the appropriate capacitance in series with the motor.

1. What value is that capacitance?

2. Operated at 120 V_rms, what is the rms current through the motor when operated at 60 Hz?

3. In France, where the frequency is 50 Hz, by how much will the operating current decrease?

4. What is the power factor of the motor in France?

5. What capacitance should be added in parallel to the existing capacitor to bring the power factor back to unity?

After a few weeks in France, you start to develop a craving to see an episode of South Park. Unfortunately there is no cable in your room; however, you do spot an old television antenna on the roof of your building. The antenna is about 10 m away; you recall that Channel 3 is transmitted at a frequency of 60 MHz, which would correspond to a wavelength of 5 m in free space. Thus the correct transmission line is going to be needed to connect the antenna to a TV in your room since the distance is larger than the wavelength.

The easiest transmission line geometry to construct for this application is the twin-lead comprised of two parallel wires of radius a separated by a fixed distance d. (You studied this geometry in a special homework problem.) Recently I demonstrated that the inductance per unit length is L₀ = (mu₀/pi) ln[(d-a)/a].

1. Use Gauss's law and superposition to find an expression for the electric field at a point between two long parallel conductors, if oppositely charged.

2. From the result of part a), find an expression for the potential difference between the two conductors.

3. From the result of part b), find an expression for C₀, the capacitance per unit length.

4. What ratio of d/a would be required for the characteristic impedance of the twin-lead transmission line to be 300 ohm?