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Unformatted text preview: Physics 171.102
Midterm Exam 3 April 29, 2011 Answer all four problems. Be sure that you pace yourself so that you have enough time
to work on each problem. Make sure that your answers are clearly marked, for example by drawing a box around
them. In all cases, do not simply write down an answer but show your work or explain
your solution. Partial credit will be given, so be sure to show your work as clearly as
possible. Only work written in your blue book will be graded. Honor Pledge. Before turning in your exam, please write out and sign & date the
following pledge: “I have completed this exam without unauthorized assistance from any person,
materials, or device.” Good luck! List of potentially useful formulae Ampere’s Law: 9513’ dE = ,uor' enclosed Faraday’s Law: 5 = 95E  dE = —%
t
Mechanical Work: W = FdE
. ‘ di] . _ di
Mutual Inductance. 512 = —M21 d— Self Inductance. .9 = —Ld—
r t
lmpedances: resistor: XR = R inductor: XL = de capacitor: X1: I/de Potential Energy in Inductor: U= $11232 8 For series RLC circuit driven by AC EMF source: 1 = Wm—m
[R2 + (XL “ Xcﬂ
d) 2 atrial/(M)
' R
Maxwell’s Equations: 95E  d‘ = gem’o‘ed gSE dz? = 0
“30
~ d¢ » dd} .
ﬁE ' f = _d—IB §B I d3. = SUMO E + IMOZenclosed For an electromagnetic wave in vacuum: w/k = c Poynting Vector: E = LE x E
#0 Intensity: I = Savg
Sneli’s Law: n1 Sin 81 = r12 sin 92
Brewster Angle: 63 = arctan(n2 H11)
cos(60)=1/2 cos(30) = «IE/2
sin(60) = 45/2 sin(30) = 1/2 cos(45) = Ji/z sin(45) = «Ii/2 time average: <sin2(cot)> = (cos2(mt)) =§ Problem 1 (25 points) A metal wire bent into a circle of radius a is placed in a uniform magnetic field B and is
spun at a constant angular velocity (u (where a) is in radians/second), as shown in the picture below. The wire has a resistance R. (a) Derive an expression for the magnetic flux passing through the circle as a
function of time. (b) Due to the changing magnetic flux, a timevarying current is induced in the wire.
What is the peak amplitude of this current? (0) How much work is required to rotate the wire through one revolution? Problem 2 (20 points) Consider an electromagnetic wave traveling through a material with index of refraction
n. The wave has a magnetic field of the form: 3 = Bmsin(k:y + wtkfc where it: 0001 m'1 and a) = 2x105 3‘1. (Recall that the speed of light in vacuum is
3x108 We). (a) What is direction of the Poynting vector? (b) Imagine that the wave is incident on a polarizer whose polarization axis makes
an angle of 30° to the xaxis. What fraction of the incident wave intensity does
the transmitted wave have? (c) What is material’s index of refraction? Problem 3 (30 points):
Consider the circuit depicted below containing a battery with emf V0, a switch, an
inductor with inductance L, and three identical resistors with resistance R. The currents
through two of the resistors are labeled i1 and i2, as shown. The switch has been left
open a long time. For questions (a) — (c), express your answers in terms of V0, L and Ft.
(a) What are i; and i2 immediately after the switch is closed?
(b) What are i1 and 32 a long time after the switch is closed?
(0) After the switch has been closed for a long time, it is reopened. What are the changes in i1 and i2 upon reopening the switch? imagine now that the resistors alt have a value of 5 Q and that the battery’s emf is 10 V.
in altime t = 0.07 seconds after the switch is reopened, l2 has fallen to exactly half the
value it had immediately after it was opened. (d) What is L in Henrys? (in calculating L, use the approximation ln(0.5) a: 0.7.) (e) How much energy in Joules is dissipated by the resistors in the first 0.07 seconds
after the switch is reopened? Problem 4 (25 points) For each of the following three short problems be sure to explain your answer in order
to earn full credit.  (a) (8 points) The graph below displays the voltage across a capacitor whose plates
are connected through an inductor as a function of time for two LC circuits
labeled A (solid line) and B (dashed line). The capacitors in the two circuits are
identicat. For each of the following, is the quantity greater in A, greater in B, or
equal in the two circuits? (i) The maximum charge on the capacitor
(ii) The inductance
(iii) The maximum current (b) (7 points) An isotropic light source is placed 1 meter below the surface of a pool
of oil with index of refraction n = 2. What is the diameter of the circle on the
surface of the oil through which light is transmitted into the air above? (0) (10 points) Consider a resistor of value 100 9, an inductor of value 0.1 H, and a
capacitor of value 10 HF connected in series to an AC generator with an emf of
103in(u)dt) Votts. The driving frequency rod is adjusted so that the circuit is in
resonance. (i) What is rod? (ii) What is the amplitude of the current? (iii) By what phase angle does the current lead the source voltage? (iv) What is the amplitude of the oscillating potentiat drop across the inductor? ...
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 Fall '08
 bennet
 Energy, Magnetic Field, long time, Inductor

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