November 16, 1992 Midterm Exam 2

This is a closed book exam; however, one 3" x 5" notecard is permitted.

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.** *20 points* -- Short-answer questions:

**a.** Consider a *velocity selector* that consists of perpendicular, uniform
electric and magnetic fields, with the **B** field directed straight up.
A beam of positively charged particles passing through the velocity selector from left to
right is undeflected by the fields (**F**_{mag} equal and oppositely-directed
to **F**_{el}).

- In which direction is the electric field?
The direction of the particle beam is now reversed to that it travels from right to left.

- IS the beam deflected now? If so, in which direction?
Now a beam of

*electrons*having the same velocity is passed through the crossed fields, once again from left to right. - Is the electron beam deflected? If so, in which direction?

**b.** Two conducting loops with a common axis are placed near each other as shown.
Initially the currents in both loops are zero. Suddenly a current *i _{a}* is set
up in loop

- In which direcion in the current induced in loop
*b*? - What is the direction of the force that loop
*a*exerts on loop*b*?

**c.** Correct the following *incorrect* statements by inserting a word or
a phrase. You need not rewrite the entire statement.

- The emf induced in a circuit is proportional to the magnetic flux through the circuit.
- Lenz's law states that the direction of an induced emf is always opposite to the magnetic field that induced it.
- The magnitude of a magnetic field varies with the square of the distance from the current element that creates the field.

**2.** *30 points*

Coaxial cable is typically used to make high-speed circuit connections
between electronic test instruments.
RG58/U cable consists of an inner wire of diameter *a* = 0.81 mm,
surrounded by polyethylene,
a concentric conducting braid of diameter *b* = 2.9 mm,
and insulation, as shown in the figure.
*Evaluate the inductance per meter length.*

**a.** Use Ampere's law to determine the magnetic field at a point between
the long coaxial conductors when equal but oppositely-directed current flow (*a<r<b*).

**b.** Use the result of part **a** to find the magnetic energy *density*
between the conductors.

**c.** Now find an expression for the total magnetic energy stored between the
conductors per length *l*.

**d.** Express the inductance per length *l* of a coaxial cable in terms of the
cable parameters, *a* and *b*, using the result of part **c**.

**e.** Evaluate the inductance per meter length of RG58/U cable.
(How many microH/m)?

**3.** *20 points*

Consider two *long* parallel wires separated by a distance *d* and carrying currents
*i _{a}* and

- Derive an expression for the magnetic field arising from
*i*, located at wire_{a}*b*.**Indicate its direction.** - Derive an expression for the magnetic force per unit length
*l*on wire*b*that results from the magnetic field above.**Indicate its direction.** - Evaluate the force per meter length if the separation
*d*is 1.0 mm and both currents are 10 A.

**a.** The flashing lights seen on barricades at street work and construction sites are criven
by a relaxation oscillator circuit as shown in the figure, with *N* being a neon
lamp. The lamp is nonconducting until the voltage across it (And the capacitor also)
rises to a value of 45 V whereupon it "ignites," dropping its resistance almost instantly
to zero and discharging the capacitor. Then the lamp again becomes nonconducting and the
process repeats.

If the *emf* = 60 V and C = 0.10 microF,
what should *R* be for the lamp to flash every 1.5 sec?

**b.** By direct integration of *dU*/*dt* = *i ^{2}R*,
prove that when switch

"http://www.physics.udel.edu/~watson/phys208/exams/mid2-92f.html"

Last updated Dec. 15, 1997.

Copyright George Watson, Univ. of Delaware, 1997.