Answer Set 4
1.
K
M
J
M
un
K
vn
M
J
u n+1
M
K
vn+1
The energy of this system is
U=
1
2
n
[J(vn un )2 + K(un+1 vn )2 ].
The equations of motion come from dierentiating U:
M un = force on atom at un =
Answer Set 9
Physics 140B
1. Cylinder b) is aligned with the magnetic eld and hence distorts the eld less. This means that
for a given applied eld, the maximum total eld (which occurs near the sides o
Answer Set 3, Physics 140A
1. Since the bi s are primitive vectors of the reciprocal lattice, the unit cell volume is |b1 (b2 b3 )| =
2
( |a1 (a2 a3 )| )3 |(a2 a3 ) [(a1 a3 ) (a1 a2 )]|. From the BAC-
Answer Set 8
Physics 140B
1. a) I didnt specify the saturation magnetization, but Ill assume that the hysteresis loop is almost closed
at 3 Tesla, which means the remanent magnetization is about 2.1 T
Answer Set 7
Physics 140B
G&S 9.9: From (9.23), Msat = ngB J = nm = n(4B ). The numbers in the problem show
n = 8/(0.839 109 )3 /m3 , or 1.4 1028 /m3 . This gives Msat = 5.0 105 A/m, close to the
obse
Problem Set 9
Physics 140B
Due Wednesday June 9, 2004: no late homework accepted
1. Two identical superconducting cylinders (i.e., same shape, same size, same material) are placed
in a magnetic eld as
Problem Set 8
Physics 140B
Due Friday May 28, 2004
1. a) Sketch the hysteresis loop from ramping a eld up to 3 Tesla and down to -3 Tesla, if the
loop has squareness 0.7 and coercive eld 1 Tesla. You
Answer Set 6
Physics 140B
G&S 9.5: As x 0, with the expansion on p. 281 coth
J+1
3J x.
From this, = (ngB J) J+1 gB Jo =
3J
kB T
3n
G&S 9.11: From equation (9.59), P = o 2 ( 2EF ) =
B
P
(9.25), the ra
Answer Set 4
Physics 140B
1. a) The electric eld runs perpendicular to the interface; call it the x direction. Its magnitude
x
is zero except for dp x dn and is given by E(x) = dp dx 4 (x ). Hence E(x
Problem Set 5
Physics 140B
Due Friday May 7, 2004: no late homework accepted
1. a) Sketch the output voltage as a function of input voltage, for -1 V Vin 1 V.
R
n
p
V
out
V in
p
n
R
b) Repeat a) if th
Problem Set 7
Physics 140B
Due Friday May 21, 2004
Do G&S 9.9, plus the following:
1. (after Kittel problem 15.5)
Consider a small spherical single-domain particle of a uniaxial ferromagnet, with magn
Problem Set 6
Physics 140B
Due Friday May 14, 2004
Do G&S 9.5 and 9.11, plus the following:
1. a) Following Hunds rules, what are the total S, L, and J for a holmium atom, a Ho3+ ion, a
yttrium atom,
Answer Set 5
Physics 140B
1. a) This time Vout = |Vin |, since the voltage measurement has positive in opposite directions
for the two resistors. (Im dening the upper output terminal as negative for t
Answer Set 3
Physics 140B
m
G&S 11.2: The change in is = 3 kB T ln mhds . Using the conversion that kB T at 300 K is 25 meV
4
eds
gives = 11 meV. (The chemical potential goes down because the conducti
Answer Set 1
Physics 140B
1. a) Constant-energy curves are concentric spheres. Note that dE = 3k 2 dk. The k-space volume
between spheres at energy E and E + dE is 4k 2 dk = 4( dE . The k-space volume
Answer Set 2, Physics 140B
1. a) Dual lattice atoms at the centers of each triangle in the original lattice gives a honeycomb lattice.
b) There is a path across a random triangle lattice if and only i
Problem Set 2
Physics 140B
Due Friday, April 16, 2004
1. a) What lattice is dual to the triangle lattice for bond percolation? You can just sketch the
lattice if you dont know its name.
b) What does t
Problem Set 1
Physics 140B
Due Friday April 9, 2004
1. The concept of density of states, from last term, is crucial for connecting theoretical calculations
with actual measurements. This question give
Problem Set 4
Physics 140B
Due Friday April 30, 2004
1. a) Find the electric eld for the charge distribution near a pn junction shown in Figure 11.28
and discussed in class. Assume a charge density eN
Supplemental Problems for Physics 7A
v1.0; 10/2010
Chapter 1
1. An insulated box contains 10 g of ice at -10oC. 1 g of steam at 110oC is injected into the box.
Once thermal equilibrium is achieved, th
7A Sample Quiz 1
No books or notes. Calculators OK. Show all your work below. Answers alone do not receive credit!
1) A glass of ice-water is a mixture of ice cubes and water that has a temperature of
Supplemental Problems for Physics 7A
v1.0; 10/2010
Chapter 1
1.
a) Decreasing energy systems: Eth of steam, Eb of steam, Eth of condensed water.
Increasing energy systems: Eth of ice, Eb of ice, Eth o
A skier weighing 55 kg skis down a hill. The skier starts from rest at the top of a hill. (The hill has a
height of 10 m and is covered in snow.) When the ski
How do bonds form?
1) Imagine that two particles which can interact via the Lennard-Jones pairwise potential are
separated by a very large distance (r > r0), so that they have zero potential energy, a
Physics 7 multiple choice problems
(From David Webbs Physics 7A C/D course 2011 )
Concept Group 1
1. What kind of reaction happened when you triggered a heat pack at
Counting Energy Modes in Multiple Ways
At room temperature, an O2 gas with N particles has 5*N thermal energy modes as determined
by its heat capacity. Since O2 is a linear molecule, these can be iden
7A Quiz 3
Last 6 digits of ID #
Name:
S Reaction
HgSignature:
DL Sec.
No books or notes. Calculators OK. Show all your work below. Answers alone do not receive credit!
Pure liquid mercury (Hg), and pu
How Microwaves Work
1. Develop an explanation for how microwaves heat food. What modes are relevant
and how are they relevant?
2. Consider the molecule shown below. The Potential Energy (PE) of this m