October 11, 1993 Midterm Exam 1
This is a closed book exam; neither notes nor formula cards (including those stored in programmable calculators) may be referred to during the exam.
Since the exam booklet is separated for grading; it is important to:
Please read questions carefully.
Credit may be lost inadvertently if solutions are not neat and orderly.
Be careful with units, signs, and significant figures.
Some possibly useful constants:
1. 30 points  Shortanswer questions:
a. For each of the following 4 statements, provide a counterexample to show that it is FALSE.
b. Two identical capacitors, connected in parallel, are charged by a battery which is then disconnected. When a dielectric is inserted between the plates of capacitor A, with capacitor B remaining empty, which way does charge flow? (To B from A, or to A from B?) Explain briefly.
c. Discuss thoroughly, yet concisely, the electrostatics of a charged conductor.
2. 35 points
Consider the following circuit that might represent a flashlight, four identical Dcells connected in pairs as shown. Each Dcell provides an emf of 1.5 V and has an internal resistance r of 0.2 ohms; the lamp has resistance R = 7.0 ohms.
a. What is the current through the lamp? b. Confirm Kirchhoff's loop rule for the outside loop. c. What is the power dissipated by the lamp? d. If the current is measured to an accuracy of 2% and the resistance is known only to within 5%, what will the uncertainty of the power calculated above be (in percent)? 

e. The polarity of one of the Dcells is switched. Now what is the current through the lamp? 
3. 35 points
a. Use Gauss's law to determine the electric field at a point between the two conducting shells when oppositely charged. Be sure to show the gaussian surface used and indicate the direction of the resulting field.
b. Use the resulting electric field to find the energy density u_{E} in the region between the conductors and then the total energy U stored by the capacitor.
c. Express the capacitance in terms of the parameters of the capacitor shown, by using U = Q^{2}/2C.
d. Evaluate the capacitance if a = 10 mm, b = 11 mm, c = 12 mm, and d = 13 mm.
e. A simple check of your true understanding of conductors and Gauss's law:
If identical charges are deposited on both conductors, say +1 microcoulombs, how are the charges distributed among the four surfaces?