Jan 13, 2000

Notes for Lecture Notes for Lecture #1

1  Introduction

  1. Textbook and course structure
  2. Motivation
  3. Chapters I and 1 and Appendix of Jackson

    1. Units - SI vs Gaussian
    2. Laplace and Poisson Equations
    3. Green's Theorm

2  Units - SI vs Gaussian

Coulomb's law has the form:

F = KC q1 q2
r122
 .
(1)
Ampere's law has the form:
F = KA i1 i2
r122
   ds1 ×ds2 × ^
r
 
 12,
(2)
where the current and charge are related by i1 = dq1/dt for all unit systems. The two constants KC and KA are related so that their ratio KC/KA has the units of (m/s)2 and it is experimentally known that in both the SI and CGS (Gaussian) unit systems, it the value KC/KA = c2, where c is the speed of light.

The choices for these constants in the SI and Gaussian units are given below:

CGS (Gaussian) SI
KC 1 [1/( 4 pe0)]
KA [1/( c2)] [(m0)/( 4 p)]

Here, [(m0)/( 4 p)] º 10-7 N/A2 and [1/( 4 pe0)] = c2 ·10-7 N/A2 = 8.98755×109 N ·m2/C2.

Below is a table comparing SI and Gaussian unit systems. The fundamental units for each system are so labeled and are used to define the derived units.

Variable SI Gaussian SI/Gaussian
Unit Relation Unit Relation
length m fundamental cm fundamental 100
mass kg fundamental gm fundamental 1000
time s fundamental s fundamental 1
force N kg ·m2/s dyne gm ·cm2/s 105
current A fundamental statampere statcoulomb/s [1/ 10 c]
charge C A ·s statcoulomb Ö{dyne ·cm2} [1/ 10 c]

One advantage of the Gaussian system is that all of the field vectors: E,D,B,H,P,M have the same dimensions, and in vacuum, B = H and E = D and the dielectric and permittivity constants e and m are unitless.

CGS (Gaussian) SI
Ñ·D = 4 pr Ñ·D = r
Ñ·B = 0 Ñ·B = 0
Ñ×E = - 1/c [(B)/( t)] Ñ×E = - [(B)/( t)]
Ñ×H = [(4 p)/ c] J + 1/c [(D)/( t)] Ñ×H = J + [(D)/( t)]
F = q (E + [(v)/ c] ×B F = q (E + v ×B
u = [1/( 8 p)] (E·D+B·H)u = 1/2 (E·D+B·H)
S = [c/( 4 p)] (E ×H)S = (E ×H)

File translated from TEX by TTH, version 2.20.
On 13 Jan 2000, 09:43.