Electromagnetism before Maxwell

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Electromagnetism before Maxwell
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Coulombs Law
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Comments

• Using SI units
• ?0 is known as the permitivity of free space
• The vector r is the vector connecting the two
  points
• In general

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Faraday introduced the concept of lines of Force
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Lines of force
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Field Around a conductor
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Concept 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.
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Principle 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
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Continuous Distribution of charge

• If the charge is distributed continuously over
  some region the sum becomes an integral

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Find the electric field a distance zabove the
mid point of a straight line segment of length
2L
?
z
-L -x 0
x L
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Cross 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
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Properties
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Notation
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Properties
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a (b c) c (a b) b (c a)
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Curl
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properties
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Central Force
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Let us consider the circulation of fluid around a
differential loop in the xy plane
y
2
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x
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Laplacian
Laplaces equation
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Properties
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Closed
open
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Closed
open
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Closed
open
C1
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Closed
open
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Closed
open
C2
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Which is zero everwhere except r0 where it is
singular s.t.
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Some More Mathematics

• The Dirac Delta Function

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• 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

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• The best way to think of the delta function is
  that it is an integral waiting to happen!

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Corollary
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Fourier INTegral Theorem
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Inverse Fourier Transform
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Convolution theorem