## PHYS208 Fundamentals of Physics II

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:

• 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.

Some possibly useful constants:

1. 30 points -- Short-answer questions:

a.  For each of the following 4 statements, provide a counterexample to show that it is FALSE.

• If there is no charge in a region of space, the electric field on a surface surrounding the region must be zero everywhere.
• Gauss's law holds only for symmetric charge distributions.
• If the net charge on a conductor is zero, the charge density must be zero at every point on the surface of the conductor.
• If the electric field is zero in some region of space, the electric potential must also be zero in that region.

b.  Two identical capactitors, 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 D-cells connected in pairs as shown. Each D-cell 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 D-cells is switched. Now what is the current through the lamp?

3. 35 points

The spherical capacitor is often considered because it is finite-sized but without the complication of a fringing field, present for the parallel-plate capacitor usually considered. Find an expression for its capacitance using ENERGY CONSIDERATIONS.

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 uE 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 = Q2/2C.

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?

• #1, inner surface
• #1, outer surface
• #2, inner surface
• #2, outer surface

"http://www.physics.udel.edu/~watson/phys208/exams/mid1-93f.html"
Last updated Dec. 12, 1997.
Copyright George Watson, Univ. of Delaware, 1997.