Physics 134
Homework Set 5 Solutions
1. Lets try to find the Roche limit, the distance from a planet at which a moon would
be broken apart by tidal forces. We will make a few simplifying assumptions a
Physics 134
Homework Set 3 Solutions
1.
(a) About how many more sidereal days are there in a year than solar days (tropical
or sidereal year is immaterial here)?
At the level of accuracy expected here
Physics 134
Homework Set 2 Solutions
1. Describe how you would go about finding the star Mirfak which lies in the constelation Perseus at Decl. 49 52m ; R.A. 3h 24m in the sky in Durham on February 3
Physics 134
Homework Set 4
Due 9/22/17
1. Comets orbit the Sun, as we mentioned, in highly elliptical orbits. Lets see how
elliptical, using Keplers laws.
(a) Halleys comet orbits with a sidereal peri
Notes on Eigenvalues
Math 107 - Summer 2012
Eigenvalues and Eigenvectors
Definition: Given a square matrix A we define its eigenvalues and eigenvectors through
the following equation,
Av = v
The numbe
Key ideas and formulas for statistical physics
(overlaps with Ch6 of Philip Nelsons Biological Physics)
Goal: to characterize macroscopic systems consisting of many microscopic
parts such that the mac
Diagonalization, Transformation, Generators and Commutators
Phy 464 - Fall 2013
In this note we focus on topics specifically pertinent to quantum mechanics. Please consult
the note Eigenvalues and Eig
Jim Lambers
MAT 415/515
Fall Semester 2013-14
Lecture 3 Notes
These notes correspond to Section 5.2 in the text.
Gram-Schmidt Orthogonalization
We have seen that it can be very convenient to have an o
Postulates of Quantum Mechanics and Discrete Systems
Phy 464 - Fall 2014
In this note we discuss the basic postulates and properties of quantum mechanics and show
their application to some discrete sy
a) The wire is equipotential.
F
because it carries a current and has a finite conductivity and thus has a nonzero electric field inside.
b) If one doubles the current I through the wires, the electric
As always, a conductor in electrostatic equilibrium:
has no electric field inside or tangent to the surface;
is equipotential, as one can move a small test charge around through zero field doing no
y
dQ
d
R
dE x
dE
x
dEy
A quarter of a ring of total charge Q and radius R is oriented as shown in the figure above. Find the electric
field at the origin (magnitude and direction) from direct integrat
1
2
I1
I3
1
I2
3
6V
2
4V
Suppose we (more or less randomly) assign the directions above to the unknown currents. In that case the
junction rule is:
I1 = I2 + I3
We can evaluate the loop rule for the t
negative charge closer than positive charge
+
+
+
E=0
+
+
+
+
+q
F
Eext
Even though there is no net charge on the conducting sphere, there is inexhaustible negative and positive free
charge that rearr
e+
F
v
B
e
~ (for a positive charge) we see that a force will deflect the positive positron
Using the right-hand rule for ~
vB
~
to the left if B is:
a) into
the page.
Fm
q
E down, B in
v
Fe
The elect
F1
+q
F1
F2
a
q
+q x
a
The magnitude of the force from the horizontal and vertical corner charges is just:
ke q 2
a2
The directions are vertically up (from the lower right hand corner) and to the righ
b
a
+
V
Assume that the voltage puts a charge Q on the inner conducting shell and Q on the outer shell. From Gausss
Law:
ke Q
Er = 2
r
and the potential difference between the two shells is:
V = V =
k
y
Q
R
x
A quarter of a ring of total charge Q and radius R is oriented as shown in the figure above. Find the electric
field at the origin (magnitude and direction) from direct integration. Show all w
R
C
+Q0
L
At time t = 0 the capacitor in the LRC circuit above has a charge Q0 and the current in the wire is I0 = 0
(there is no current in the wire).
a) Find (or remember) Q(t). Dont forget to defin
magnetic field ends
hand
Bin
R
A conducting loop of wire with a small but finite resistance R sits in and perpendicular to a powerful magnetic
field that ends at the left edge of the wire loop as show
B
A
+Q
A charge Q sits close to the inner surface of a hollow conductor in electrostatic equilibrium as shown above. Is the
potential at A:
a) Greater than the potential at B.
b) Equal to the potentia
z
a
I
A circular loop of wire of radius a is carrying a current I counterclockwise (viewed from above) around the
z-axis. It is located in the x-y plane, centered on the origin as drawn.
a) Using the
Problem 1.
B(uniform)
I
I
30
a
I
b
c
In the figure above, three wire (segments) are shown, each of length , each carrying a current I, in a uniform
magnetic field. Under or on each figure indicate:
a)
Find the capacitance of this arrangement any way you like.
Note well, this is equivalent to two capacitors in parallel with area A/2 and plate separation d. Thus the easiest
way is to use the two rule
A/2
A/2
+Q
d
1
2
Q
In the figure above, a parallel plate capacitor with cross-sectional area A and plate separation d is drawn. The space
between the plates is filled with two dielectrics with relativ
I(t)
a
b
d
r
R
In the figure above, I(t) = I0 sin(t) in the long, straight wire to the left. A rectangular conducting loop of
resistance R, width a and length b sits a distance d from and in the plane
R
I
a
b
In the picture above, a circular capacitor is being charged by a current I. Using Amperes Law and the Maxwell
Displacement Current, derive a formula for the magnitude of the magnetic field at
b
a
+
V
A spherical capacitor has inner radius a and outer radius b
Find the capacitance of this arrangement. Show All Work!
Show that when b = a + with a the capacitance has the limiting form C = 0
2q
+a
q
+a
q
2q
Find the total potential energy of the arrangement of four charges above.
2q
+a
q
+a
q
2q
What is the potential at the center of the square of four charges shown (at the origin)? Note