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:
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 (Fmag equal and oppositely-directed to Fel).
The direction of the particle beam is now reversed to that it travels from right to left.
Now a beam of electrons having the same velocity is passed through the crossed fields, once again from left to right.
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 ia is set up in loop a, with direction as shown.
c. Correct the following incorrect statements by inserting a word or a phrase. You need not rewrite the entire statement.
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 ia and ib in the same direction.
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 = i2R, prove that when switch S is thrown from a to b in the circuit below, all the energy stored in the inductor appears as thermal energy in the resistor.