NAME:___________________________

Recitation section number (or day/time):___________________________

PHYS208 First Midterm Exam October 10, 1997

This is a closed book exam; the formula sheet provided is 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.

Since this exam booklet may be separated for grading; it is important to:

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

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

Be careful with units, signs, and significant figures.

1. (30 points)

1. State Gauss's law in words, carefully and concisely.

2. Two capacitors are identical except that the region between the plates of capacitor A is filled with a dielectric and B is empty. These capacitors are connected in series to a battery.

• Does capacitor A have a potential difference that is smaller, the same, or larger than that of capacitor B? Briefly state your reasoning.

• Imagine that the battery is first disconnected, followed by removal of the dielectric from capacitor A and insertion into capacitor B. Describe any changes in charge or potential difference.

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

4. Two lamps A and B of identical resistance are connected in series to a battery having negligible internal resistance -- each lamp glows with the same intensity (proportional to the power dissipated by it). Lamp A is suddenly shorted out by connecting a wire of negligible resistance across its terminals. Specify as completely as possible what happens to the intensity of each lamp.

5. The formula for the resistance of a cylinder demonstrates that the current density is uniform across the cylinder, not accumulated at the surface. Why?

2. (40 points)

 Consider the following circuit that represents a small penlight, one alkaline AAA cell connected to a lamp. The AAA cell provides an e1 of 1.5 V and has an internal resistance r1 of 0.6 ohms. The lamp resistance R is 7.0 ohms. What is the current in the circuit? What is the terminal voltage of the AAA cell? In an attempt to increase the brightness of the lamp, an enthusiastic child finds a new 9 V lithium battery and adds it in parallel to the lamp and AAA cell as shown. If the current in the lamp is now 0.23 A, please answer the following questions: What is the terminal voltage of the AAA cell now? What is the internal resistance of the 9 V battery? Was it worth it? (Consider power delivered and dissipated in each element.) 3. (30 points)

A conducting sphere of radius R has an excess charge +Q.

1. Demonstrate as thoroughly as possible the application of Gauss's law to find the electric field at a distance r from the center of the sphere.

2. What is the electrical energy density (in terms of Q and R) associated with the electric field at this point?

3. From the result of part b, find the total electrical energy (in terms of Q and R) stored in the region surrounding the charged sphere?

4. Finally, comparing the result in part c with the energy stored in a charged capacitor, find the capacitance of a single conducting sphere of radius R.
5. Evaluate the capacitance of sphere having radius 1.0 cm. How many pF?

"http://www.physics.udel.edu/~watson/phys208/exams/mid1-97f.html"
Last updated Nov. 13, 1997.
Copyright George Watson, Univ. of Delaware, 1997.