Fall 2008
6.642 Continuum Electromechanics
Problem Set 4 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 1
a)
H = 0 H =
H = 0 2 = 0
r>R
(r, ) =
Dr +
C
r2
cos
0
1
1
H = =
ir +
i +
i
r
r
r sin
=
D
2C
r3
cos ir
1
r
Dr +
C
r2
sin i
r>R
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.642 Continuum Electromechanics
Problem Set #4
Fall Term 2008
Issued: 9/24/08
Due: 10/03/08
Problem 1
A sphere of radius R and infinite magnetic permeability
Fall 2008
6.642 Continuum Electromechanics
Problem Set 5 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 7.6.3
Mass conservation requries that
4 3 4 3
+ = 2
3 1 3 2
4 3
3 0
3
3
3
1 + 2 = 20 .
(1)
With the pressure outside the bubbles dened as p
Fall 2008
6.642 Continuum Electromechanics
Problem Set 7 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 8.12.2
Stress equilibrium at the interface requires that
+ 0 H0 he ;
R
2
p + p Trr |R+ = 0 pd = 0 H0
d
e
=
1
2
0 H0 .
2
(1)
Also, at the int
Spring 2005
6.641 Electromagnetic Fields, Forces, and Motion
Problem Set 10 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 10.1
The equation of motion for a static rod is
0=E
2
+ Fx where Fx = g
x2
We can integrate this equation directly and get
Fall 2008
6.642 Continuum Electromechanics
Problem Set 6 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 8.10.1
Figure 1: A planar layer of insulating liquid separates innite half-spaces of perfectly conducting liquid
(Image by MIT OpenCourseWare
Fall 2008
6.642 Continuum Electromechanics
Problem Set 8 - Solutions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 8.18.2
The basic equations for the magnetizable but insulating inhomogeneous uid are
v
+ v v
t
1
= p gix H 2 ,
2
(1)
v = 0,
(2)
h = 0,
(3)
6.641 Electromagnetic Fields, Forces, and Motion
Spring 2005
Problem Set 10 - Questions
Prof. Markus Zahn
MIT OpenCourseWare
Problem 10.1 (W&M Prob 9.1)
A long thin steel cable of unstressed length l is hanging from a xed support, as illustrated in Fig. 9
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.642 Continuum Electromechanics
Problem Set #5
Fall Term 2008
Issued: 10/01/08
Due: 10/10/08
Problem 1
Prob.7.6.3 (Melcher)
Problem 2
Prob. 3.10.3 (Melcher)
P
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.642 Continuum Electromechanics
Problem Set #6
Fall Term 2008
Problem 1
Prob. 8.10.1 (Melcher, Continuum Electromechanics)
Problem 2
Prob. 8.12.1 (Melcher, Co
MassachusettsInstituteofTechnology
DepartmentofElectricalEngineeringandComputerScience
6.642ContinuumElectromechanics
December10,2008
Formulasheetsarelocatedafterpage6.
1. (33points)
z
R
z =h
g = g iz
a
Surfacetension
(r )
z = 0
r
b
Twosuperposedfluid
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.642 Continuum Electromechanics
Problem Set #8
Issued: 11/25/08
Fall Term 2008
Due: 12/09/08
Suggested Reading: Sections 8.17, 8.18
Final Exam: Dec. 9, 2004,
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.642 Continuum Electromechanics
Problem Set #7
Fall Term 2008
Problem 1
Prob. 8.12.2 (Melcher, Continuum Electromechanics)
Problem 2
Prob. 8.13.2 (Melcher, Co
6.642 Continuum Electromechanics
Fall 2008
Final Exam - Solutions 2008
Prof. Markus Zahn
MIT OpenCourseWare
Problem 1
A
Figure 1: Two superposed uids surround and wet a cylindrical rod of radius R.
Two superposed uids surround and wet a cylindrical rod of
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.641 Electromagnetic Fields, Forces, and Motion
Quiz 2
April 20, 2005
You are allowed to use a one page (both sides) formula sheet that you have prepared for
6.641, Electromagnetic Fields, Forces, and Motion
Prof. Markus Zahn
Quiz 2: Solution
1)
(a)
H = Hy iy
at 0 < x < d
at x < 0 ,
H=0
at d < x ,
(b)
H=0
( )
( )
Hy 0+ Hy 0 = Kz ( 0 )
at x = 0
( )
Hy 0+ = K0 cos t
( )
( )
Bx d+ = Bx d = 0
at x = d
( )
Hy d =