NAME:___________________________

Recitation section number (or day/time):___________________________

### PHYS208 Second Midterm Exam       November 14, 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. (25 points)

1. State Lenz's law in your own words, carefully and concisely.

2. A current loop is held in place above a bar magnet as shown. Is the force between the two objects repulsive or attractive? Briefly explain.

3. In a uniform magnetic field that points toward you, will an electron circulate clockwise or counterclockwise? (Include sketch showing magnetic field and force.)

4. In the classroom demonstration using the CRT of an oscilloscope, what direction of the applied magnetic field deflected the electron beam upward? (Include sketch.)

5. Three long straight wires with identical currents, one directed oppositely, are used to create a magnetic field. Which configuration will create the largest magnetic field at point P, which is the same distance from each wire? (Show fields!)

2. (15 points)

In the spirit of inquiry, an enthusiastic PHYS208 student creates an "energizer" flashlight by combining a new lithium battery (9.0 V, 18 ohm internal resistance), a flashlight bulb (7.0 ohm), and a coil of wire with 12 mH inductance as shown. The maximum instantaneous current that the bulb can endure without burning out is 450 mA.

1. What is the current in the bulb just at the instant that the switch is closed?

2. What is the current in the bulb a long time after the switch is closed?

3. What is the current in the bulb immediately after the switch is re-opened?

4. Describe in words the sequence of bulb brightnesses as the switch is closed and then re-opened.

3. (10 points)

After the switch is closed, how long will it take the same lithium battery to charge a 3500 microF capacitor to 99% of its final stored charge separation?

4. (25 points)

Evaluate the contribution to self-inductance of the magnetic field inside a current-carrying wire:

1. Demonstrate as thoroughly as possible the application of Ampere's law to find the magnetic field at a point inside a wire of radius R. (Be sure to sketch amperian loop and specify all directions!)

2. Use the result of part a to find an expression for the magnetic energy density inside the wire.

3. Use the result of part b to find the total magnetic energy stored inside the wire per length l.

4. Use the result of part c to find an expression for the internal inductance per length l of a wire.

5. Evaluate the internal inductance of a 10 cm length of 18-gauge wire (diameter 1.0 mm).

5. (25 points)

A vertical square loop (side 5 cm) formed from 18-gauge copper wire is falling into a region of magnetic field strength 2.4 T directed horizontally as shown. The loop reaches its terminal velocity before falling completely into the magnetic field.

1. Is the current induced in the loop clockwise or counterclockwise? Briefly provide reasoning.

2. What is the direction of the force exerted on the bottom segment of the loop?

3. Determine a formula for the current induced in this falling loop in terms of its velocity. Show work.

4. Determine a formula for the terminal velocity of this loop. Show work.

5. What is the value of the terminal velocity of this loop?

6. What is the value of the current induced in this loop?

Note: 18-gauge copper wire with insulation removed has a mass per unit length of 74 mg/cm and a resistance per unit length of 205 micro-ohm/cm.

"http://www.physics.udel.edu/~watson/phys208/exams/mid2-97f.html"
Last updated Nov. 17, 1997.
Copyright George Watson, Univ. of Delaware, 1997.