NAME:___________________________
Recitation section number (or day/time):___________________________
PHYS208 Second Midterm Exam May 1, 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.
Please read questions carefully.
Credit may be lost inadvertently if solutions are not neat and orderly.
Be careful with units, signs, and significant figures.
1. (20 points)
2. (40 points)
Consider a toroid of square cross section,
with inner radius a = 2.0 cm
and outer radius b = 3.0 cm,
consisting of 125 turns of 18gauge wire.
In a recent quiz, you determined that the magnetic field inside an energized toroid is
where r is the distance from the axis. From that result we derived that the inductance of a rectangular toroid is





3. (20 points)
Given a long straight wire of radius a carrying a uniformlydistributed current, apply Ampere’s law to find an expression for the magnetic field inside\ the wire at a distance r from its center. Please include a sketch showing the wire and direction of current, magnetic field lines with directions, and the amperian loop used.
4. (20 points)
Recently in class the above result was used to determine the contribution of the "internal" field to the selfinductance. By using energy considerations I showed that its contribution per unit length was
Rather than repeat that same calculation, consider instead the case of a wire with a nonuniform current density given by j = j_{0} r/a. In one of our homework exercises, it was shown that the magnetic field inside the wire could be expressed as
Use this result (no need to rederive it!) to evaluate the "internal" contribution to the inductance per unit length in this "unusual" wire. How does it compare to the value for an ordinary wire?