3.012 Quiz 1 thermodynamics solutions
09.23.04
100 points total
3.012
Fall 2004
Thermodynamics (50 points total):
1. Consider a thermodynamic system consisting of 1 mole of the material examined in problem
3- (alumina, Al2O3)- in the solid state, reversib
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics
Problem Set #2
Spring 09
Posted Feb. 17, 2009 Due Wednesday, Feb. 25, 2009
1. Wiper speed control Design an optical system which can detect the amount
of water present on a cars windshield (see the schemat
6.013/ESD.013J Electromagnetics and Applications
Fall 2005
Problem Set 6 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 6.1
A
(Jf Jf )/t
Jf /t
= 2Jf Jf /t
2
= p E
=
2
(Jf Jf ) = 2Jf p E
t
Noting that E Jf = wk /t, we have that
wk
2 wk
(Jf Jf )
3.032 Problem Set 6
Fall 2006
ue: 11 22 06 ; no lecture on 11 22 06
1. When engineers decided that, indeed, dislocations must exist in crystalline materials, several
new questions emerged.
(a) For example, experimentally it is known that crystalline mater
2.71 Optics
Quiz 2 Solutions
Spring 09
1. Solution:
n
z
o
g1 (x, z) = a1 exp i2
sin + cos
,
6
6
n
x
o
z
g2 (x, z) = a2 exp i2
sin + cos
,
3
3
At z = 0,
x
a1 = 1
a2 =
x 1
x
1
2
p
3
2
I(x) = |g1 (x, 0) + g2 (x, 0)|2 = a1 ei2 2 + a2 e i2 2
"
p !#
2a1 a2
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Problem Set #9
Issued: 11/9/05
Fall Term 2005
Due: 11/23/05
Suggested Reading Assignment: Chapters 4 and 8.
Quiz 2 will
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics
Problem Set #3
Spring 09
Posted Feb. 23, 2009 Due Wednesday, March 4, 2009
1. Wandas world Your goldsh Wanda happens to be situated at the center of
her spherical waterworld. At the same time, your friend
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics
QUIZ 2
Spring 09
Monday, April 27th , 2009
1. Interference Two plane waves of wavelength
are propagating on the xz
plane such that their electric elds at (x = 0, z = 0) reach simultaneously their
maximum p
3.032 Problem Set 5
Fall 2006
ue: Start of lecture, 10 27 06
1. The potential energy between ions can be expressed as an equation from which the equilibrium spacing between ions ro and the binding energy between ions Ub can be determined. Here, you will c
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Problem Set #6
Fall Term 2005
Issued: 10/12/05
Due: 10/26/05
_
Reading Assignment:
Quiz 1: Thursday, Oct. 20, 2005 in l
6.013/ESD.013J Electromagnetics and Applications
Fall 2005
Problem Set 5 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 5.1
A
= D = E =
H = E =
t
x
+y
+
z
x
y
z
E0 (xx + yy) sin t = 2E0 sin t
x
y
z
x
y
x
y
z
x
y
Ex
Ey
Ez
x
y
=
z
y
x
0 E0 sin
6.013/ESD.013J Electromagnetics and Applications
Fall 2005
Problem Set 9 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 9.1
A
H=
I
2r
B=
0 I
2r
I
2r
L(h) =
b
ln a
[0 (l h) + (h + s)]
2
in free space
in uid
B
C
fx =
b
ln a I 2
1 2 dL(h)
I
=