EXAM 3 December 3, 1987 PS 208
If you need a constant not given here or do not understand a
problem, please ask me about it. No notes, books, etc. may be
used during this exam.
2 -19
g = 9.8 m/sec e = 1.6 x 10 C
9 2 2
1/ (4 pi epsilon ) = 9.0 x 10 N m / C
0
-31
The mass of the electron is 9.11 x 10 kg.
1. Magnetic transducers are often used to monitor small
vibrations. For example, the end of a vibrating bar may be
attached to an N-loop coil which in turn vibrates in and out of a uniform
magnetic field B, as shown in the ___________
figure to the right. Show that |X X X | <----
the speed of the end of the bar, |X X X |
dx/dt, is related to the EMF |___________| ----->
induced in the coil by
E = N B b dx/dt .
2. A straight wire of radius a placed along the axis of
a cylindrical metal shell with inner radius b and outer radius c ,
carries a current I. The shell carries a current
I in a direction opposite to that in the wire. Find the magnetic
field B for a < r < b and also for r > c . Coaxial cables of this
type are used widely to minimize unwanted magnetic effects.
3. (From homework) A resistor R and an inductor L are
connected in parallel across an AC generator. The source
EMF is E = E sin (omega t). Determine
0
the current through the resistor and the inductor (including
amplitude and phase) as a function of time. What is the total
current leaving the source (you need not make I algebraically
tot
pretty; any correct expression is acceptable).
4. So-called Helmholtz coils are sometimes used to obtain a
uniform magnetic field in
situations where a solenoid would be <----L---->
impractical. Two coils of radius a,
placed as shown in the figure to the O ---P--- O
right, are used. Show that, if ^ coil of radius a
L = a, then B at the point P has the value perpendicular to line
2
mu I a
0 2 2 -3/2 2 2 -3/2
B = --------- [ (a + x ) + (2a - 2ax + x ) ]
2