1
Outline of solutions to Homework 1
Problem 1.3: For convenience we place the cube with one corner at the origin and the cube in the positive
quadrant. Then the vectors of the two body diagonals are b1 = (1, 1, 1) and b2 = (1, 1, 1). The angle between th
1
PHY481 - Lecture 7: The electrostatic potential and potential energy
Griths: Chapter 2
B. Electric potential energy and electric potential
Physical denition
The electric potential energy (U) is the potential energy due to the electrostatic force. As alw
1
PHY481 - Lecture 8: Energy in a charge distribution, capacitance
Griths: Chapter 2
The potential energy of a charge distribution
The potential energy required to place a small charge q at position r is U = qV (r). We can generalize this to a
continuum f
1
PHY481 - Lecture 9: Boundary conditions and forces at charged
surfaces
Griths: Chapter 2
Energy stored in a capacitor
Since we now know that the energy is stored in the electric eld we can nd the energy by integration, ie U =
( 0 /2) u2 (r)dr For exampl
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PHY481 - Midterm I (2009)
Time allowed 50 minutes. Do all questions - to get full credit you must show your working.
The general solutions to Laplaces equation with two co-ordinates allowed to vary are:
V (x, y ) = (a + bx)(c + dy ) + k [A(k )cos(kx) +
1
PHY481 - Midterm IB (2009)
Time allowed 50 minutes. Do all questions - to get full credit you must show your working.
The general solutions to Laplaces equation with two co-ordinates allowed to vary are:
V (x, y ) = (a + bx)(c + dy ) + k [A(k )cos(kx) +
1
PHY481 - Midterm II (2009)
Time allowed 50 minutes. Do all questions - to get full credit you must show your working.
Problem 1. a) Write down the integral and dierential forms of Maxwells equations. b) Set the source terms in the
dierential forms to ze
Magnetic Charge Transport
S. T. Bramwell
1
, S. R. Giblin2 , S. Calder1 , R. Aldus1 , D. Prabhakaran3 and T. Fennell4
arXiv:0907.0956v1 [cond-mat.other] 6 Jul 2009
1. London Centre for Nanotechnology and Department of Physics and Astronomy, University
Col
1
PHY481 - Review sheet for Midterm 1
Griths: Chapters 1-3
Electric Field
There are two types of charge and they interact through Coulombs law F =
1
4
0
qQ
r2 r
=
1
4
0
qQ
r3 r.
The interaction
between many charges is found by using superposition. The ele
1
PHY481 - Lecture 6: Gausss law
Griths: Chapter 2
Electric eld lines - Faradays ideas
An extremely useful concept in developing new ideas and results in EM is the concept of electric eld lines. An
electric eld line is a series of vectors where at each po
1
PHY481 - Lecture 5: Electrostatics
Griths: Chapter 2
The basics: Coulombs law, the electric eld and superposition
Electrostatics is based on very simple principles, namely that (i) there are two types of charge, (ii) that charges
interact through Coulom
1
PHY481 - Lecture 4: Vector calculus in curvilinear co-ordinates
Griths: Chapter 1 (Pages 38-54), Also Appendix A of Griths
Scale factors h1 , h2 , h3
In general a set of curvilinear co-ordinates can be orthogonal or non-orthogonal. We focus on the ortho
1
Outline of solutions to Homework 2
Problem 2.6: By symmetry, E = (0, 0, Ez ), and by superposition we have,
Ez =
k dQ()
cos() =
r2
2
R
k
0
0
sdds
cos()
r2
(1)
where r2 = s2 + z 2 and cos() = z/r. We then have,
2
R
kz
Ez
0
0
sdds
1
1
1
= 2kz 2
|R = 2kz [
1
PHY481 - Outline of solutions to Homework 3
Problem 3.8: We consider a charge outside a conducting sphere that is neutral. In order that the sphere be neutral,
we have to introduce a new image charge Q0 = q . The solution for this case is a superpositio
1
Outline of solutions to problem set 4
Problem 5.3: a) The electric and magnetic elds are perpendicular and they are constant. Take E = E0 z and
B = B0 x and the initial velocity to be v0 y . The initial force is then,
F0 = q (E0 z + v0 B0 y x) = q (E0 v
1
Outline of solutions to Homework 5
Problem 7.1: a) We set the voltage of the inner spherical shell to be V and the potential of the outer one to be
0, so the voltage dierence is V as required. By symmetry, the current density is directed radially outwar
1
Outline of solutions to Homework 6
Problem 4.22: Since the cylinder is a uniform dielectric, the electrostatic potential obeys Laplaces equation inside
and outside. From experience, we know the solution inside corresponds to a uniform electric eld, so V
1
PHY481 - Lecture 1 (Fall 2009)
Griths: Chapter 1 (up to roughly page 10)
A. A Brief History
Early observations of magnetic and electric properties include the lodestone which is a magnetic rock and amber
that was considered special due to its ability to
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PHY481 - Lecture 2: Vector calculus
Griths: Chapter 1 (Pages 10-38)
The Gradient - A vector derivative operator
In Cartesian co-ordinates the change in a scalar function is,
df = dx
f
f
f
+ dy
+ dz
x
y
z
(1)
If we dene the gradient as the vector derivat
1
PHY481 - Lecture 3: Vector calculus
Griths: Chapter 1 (Pages 38-54), Also Appendix A of Griths
Vector calculus in three co-ordinate systems
We shall be using three orthogonal co-ordinate systems, cartesian, cylindrical and spherical polar that are dened
1
PHY481 - Review sheet for Midterm 2
Griths: Chapters 5,7 and Sections 9.2.1, 9.2.2
Static magnetic elds: Static magnetic elds are generated by DC currents or by the intrinsic magnetic moment
of elementary particles. DC current in a wire is i = il, while