November 15, 1993 Midterm Exam 2

This is a closed book exam; one 3" x 5" notecard is permitted for formulas or notes -- the notecard must be submitted with your exam solution.

Since the exam booklet is separated for grading; it is important to:

- Show ALL work on problem sheet and only on that sheet.
- Place name or initials on each examination 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.

Some possibly useful constants:

**1.** *25 points* -- Short-answer questions:

**a.** For each of the following 3 statements, provide a counterexample to show that it is *FALSE*.

- If a charged particle moves undeflected through some region of space, the magnetic field must be zero in that region.
- If a charged particle is deflected sideways when moving through a region of space, we can be sure that a magnetic field exists in that region.
- The direction of an induced emf is always opposite to the magnetic field that induced it.

**b.** An electron undergoes uniform circular motion in a uniform magnetic field.
If the field points away from you (into the page), in which direction will the electron circulate?
Include sketch for full credit.

**c.** In a certain galvanometer, with internal resistance of 50 ohm, full-scale deflection
corresponds to a current of 0.20 mA. What circuit element would convert it into an ammeter
that reads 3.0 mA full scale?

**2.** *25 points*

Fill in the table below for the circuit shown, with the switch closed at t=0. All calculations must be shown for full credit! (Note units.)

Note: the value in box (3) should be between (1) and (2).

capacitive branch | inductive branch | power supply | |

initial current (mA) | (1) | ||

final current (mA) | (2) | ||

time constant (microsec) | n/a | ||

current (mA) after 50 microsec | (3) |

**3.** *25 points*

**a.** Apply Ampere's law to find an expression for the magnetic field inside a *long* solenoid.
*Be sure to specify a direction for the current flow and the resulting magnetic field, as well as the amperian
loop used.*

**b.** Given a solenoid of length 50 cm, diameter 10 cm, 250 turns, which carries a current
of 5.0 A, evaluate the magnetic field.

**c.** If the current drops steadily to zero in 10 ms, what emf is induced in a single-turn
loop (diameter 50 cm) outside the solenoid? *Specify the direction too!*

One geometry not yet considered in PHYS208 is the so-called twin-lead, often seen in use as a lead-in wire from a
TV antenna. It consists of 2 long parallel wires of radius *a* with centers separated by distance *d*.

Evaluate the inductance per unit length by estimation as follows.

**a.** Use superposition to evaluate the magnetic field created *midway* between the wires
when the two wires carry equal but opposite currents. Please show sketch for full credit.

**b.** Estimate the magnetic flux *per unit length* permeating the area between the wires.
For this, assume a constant value of *B* at all points (the value from part **a**) for example).

**c.** Now estimate the inductance per unit length.

**d.** *For take-home portion of the exam, see following page.*

For the final 10 points of this exam, find an exact expression for **B** at all points *between*
the wires, and from that the actual inductance per unit length for a twin-lead cable.
You may neglect the flux within the wires themselves.

*Extra credit:*

5 points: Obtain the dimensions of conventional TV lead-in wire and evaluate your expression.

10 points: Correctly calculate the contribution to the inductance from the flux within the wires.

For this take-home portion, you may use any resource available to you, except for course instructors or tutors. All sources must be cited, including discussions with other students.

"http://www.physics.udel.edu/~watson/phys208/exams/mid2-93f.html"

Last updated Nov. 6, 1997.

Copyright George Watson, Univ. of Delaware, 1997.