NAME:___________________________

Recitation section number (or day/time):___________________________

PHYS208 First Midterm Exam       March 20, 1998

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.

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

Be careful with units, signs, and significant figures.

1. (20 points)

1. How are Newton's universal law of gravitation and Coulomb's law similar? How are they different?

2. An electron is released from rest in an electric field. Will it move in the direction of increasing or decreasing potential? Briefly justify your answer.

3. 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 keeping the same capacitance, which way does charge flow? (To B from A, or to A from B?) Explain clearly.

4. Two resistors A and B having identical resistance are connected in series to a battery having negligible internal resistance. Specify as completely as possible what happens to the current in A and B when a third identical resistor C is connected across resistor A. Please sketch the circuit before and after.

2. (30 points)

Coaxial cable is typically used to make high-speed circuit connections between electronic test instruments. It consists of an inner wire of diameter a, a concentric conducting braid of diameter b, separated by an insulating material. This is a capacitor geometry for which you may calculate its capacitance using Gauss's law and energy density.

1. Use Gauss's law to determine the electric field at a point between long coaxial conductors when oppositely charged. Sketch the field and gaussian surface; say a few words about the symmetry of the field and the selection of gaussian surface.
(The region between the conductors may be assumed to be empty here.)

2. Use the resulting electric field to find the energy density uE in the region between the conductors and from that the total energy UC stored by the capacitor.

3. Express the capacitance per length L of a coaxial cable in terms of the cable parameters a and b, by comparing the result of part b) with UC = Q2/2C.

4. Evaluate the capacitance per meter length of RG58/U cable, which has an inner wire of diameter 0.81 mm, an outer conductive braid of diameter 2.9 mm, and polyethylene insulating material of dielectric constant 2.25.

3. (30 points)

Your friend is having trouble starting an old car. Eager to apply your new expertise with circuits, you decide to determine the internal resistance of the battery to see if a new 12 V battery is needed. You phone your physics instructor, widely known for his generosity, and borrow a digital multimeter. You also borrow a 10 ohm resistor since you recall that the battery must be loaded to measure the effects of internal resistance, observed by connecting the resistor to the battery and measuring the change in the battery's terminal voltage.

1. What power should the resistor be able to dissipate adequately to conduct this test successfully?

 Arriving back at the car, you discover that unfortunately the voltmeter mode of the DMM has been damaged. However the ammeter mode still seems to be working so you rig the circuit shown. A current of 1.10 A is measured with the DMM. What is the internal resistance of the battery?

 While conducting this test, your friend attempts to start the car again. When the ignition switch is closed, the DMM measures a current of 0.12 A. What is the resistance of the starter motor?

4. (20 points)

 An isolated conducting ball of radius 1.0 cm has been charged by bringing it to a potential of 150 V using a power supply. Calculate the charge on the sphere. After the small ball is charged, the power supply is disconnected and the ball is then enclosed with an uncharged conducting shell (inner radius 2.0 cm and outer radius 3.0 cm). (The charge on the small ball stays unchanged.) What is the potential of the conducting shell? What is the new potential of the small ball? (Be extremely careful with your reasoning here!)

"http://www.physics.udel.edu/~watson/phys208/exams/mid1-98s.html"
Last updated March 24, 1998.
Copyright George Watson, Univ. of Delaware, 1998.