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:

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)

``Proof'' of the identity (Eq. (1.31))

Noting that

we see that we must show that

We introduce a small radius a such that:

For a fixed value of a,

If the function f(r) is continuous, we can make a Tayor expansion about the point r = r^¢. Jackson's text shows that it is necessary to keep only the leading term. The integral over the small sphere about r^¢ can be carried out analytically, by changing to a coordinate system centered at r^¢;

so that

We note that

If the infinitesimal value a is a << R, then (R² +a²)^3/2 » R³ and the right hand side of Eq. 10 is - 4 p. Therefore, Eq. 9 becomes,

which is consistent with Eq. 5.