## PHYS208 Fundamentals of Physics II

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.

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!

4. 15 points

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.