Title: Electromagnetism before Maxwell
1Electromagnetism before Maxwell
2Coulombs Law
3(No Transcript)
4(No Transcript)
5Comments
- Using SI units
- ?0 is known as the permitivity of free space
- The vector r is the vector connecting the two
points - In general
6(No Transcript)
7Faraday introduced the concept of lines of Force
8Lines of force
9(No Transcript)
10(No Transcript)
11Field Around a conductor
12(No Transcript)
13(No Transcript)
14Concept of Field
Idea Space around electric charge is altered so
if we put Another charge in the neighborhood of
the first it will experience a force.
15Principle of Superposition
The interaction between any two charges is
completely unaffected by the presence of
others. Which means to find the total field at a
point we add the field due to all the charges
16Continuous Distribution of charge
- If the charge is distributed continuously over
some region the sum becomes an integral
17 18Find the electric field a distance zabove the
mid point of a straight line segment of length
2L
?
z
-L -x 0
x L
19(No Transcript)
20(No Transcript)
21Cross Product
Let x (x1,x2,x3) and y (y1,y2,y3). The cross
product x y yields a vector perpendicular to
both x and y with direction determined by the
right-hand rule. Specifically, x y is a vector
x y (x2y3-x3y2)i - (x1y3-x3y1)j
(x1y2-x2y1)k
22Properties
23Notation
24Properties
25a (b c) c (a b) b (c a)
26Curl
27properties
28Central Force
29Let us consider the circulation of fluid around a
differential loop in the xy plane
y
2
4
x
30(No Transcript)
31(No Transcript)
32(No Transcript)
33(No Transcript)
34Laplacian
Laplaces equation
35Properties
36(No Transcript)
37(No Transcript)
38(No Transcript)
39(No Transcript)
40Closed
open
41Closed
open
42Closed
open
C1
43Closed
open
44Closed
open
C2
45(No Transcript)
46(No Transcript)
47(No Transcript)
48(No Transcript)
49Which is zero everwhere except r0 where it is
singular s.t.
50Some More Mathematics
51- It is not possible to develop a rigorous
mathematical theory of integration where such a
function exists i.e where the value of a function
at one isolated point can affect the integral
52- The best way to think of the delta function is
that it is an integral waiting to happen!
53(No Transcript)
54(No Transcript)
55(No Transcript)
56Corollary
57(No Transcript)
58(No Transcript)
59(No Transcript)
60Fourier INTegral Theorem
61Inverse Fourier Transform
62Convolution theorem