Is the Same Dynamical Theory of Electromagnetic Fields which
Transcript of Is the Same Dynamical Theory of Electromagnetic Fields which
Is the Same Dynamical Theory of Electromagnetic Fields which
Maxwell Thought is Taught today?Maxwell Thought is Taught today?
Rowdra GhatakAssociate ProfessorMicrowave and Antenna Research Laboratory, ECE DeptNational Institute of Technology Durgapur
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Birth of Cavendish Laboratory at the University of Cambridge
Duke of DevonshireWilliam Cavendish
Grandson of Henry Cavendish
Henry Cavendish1731 1810
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1731-1810
Maxwell was first Cavendish professorin Experimental Physics at Universityin Experimental Physics at University of Cambridge
J C Maxwell1831-1879
Maxwell’s lecture theatre
J J Thomson
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J J ThomsonDiscovery of electron 1897
Coulomb’s law state that the force F between two point charge Q 1 and Q 1 is1. Along the line joining them2 Directly proportional to the product Q 1 Q 12. Directly proportional to the product Q 1 Q 1
of the charges3. Inversely proportional to the square of the
distance R between them
21QkQF =
J A Coulomb
2RF
J A Coulomb1736-1806
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Gauss’s law states that the total electric flux ψ through any close surface is equal to the total charge enclosed by the surfacetotal charge enclosed by the surface.
dvdsDQ v∫ ∫=•= ρ
∫ ∫=• vdsD ρ
s v∫ ∫
Karl F Gauss1777-1855D ρ=•∇
∫ ∫s v
P i t f f th G l 1777 1855vD ρ=•∇ Point form of the Gauss law
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Biot-Savart’s law states that the magnetic field intensity dHmagnetic field intensity dHproduced at a point as shown in below by the differential current element Idl is proportional to the
d t Idl d th i f thproduct Idl and the sine of the angle α between the element and the line joining P to the element and is inversely proportional to
J B Biot1774-1862
F Savart1791-1841
y p pthe square of the distance R between P and the element.
2
sinR
IdldH ααα
dl
R
32 44 RRIdl
RaIdldH R
ππ×
=×
=
α
IP
dH
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44 RR ππ
Ampere’s circuit law states that the line integral of Haround a closed path is the same as the net current Ienc enclosed by the path.
∫∫ =• encIdlH
( ) dsHdlHIenc •×∇=•= ∫ ∫ ( )L s
enc ∫ ∫
∫ •=enc dsJI
A M Ampere
∫s
JH =×∇1775-1836
This is the differential (or point) form of Amperes law
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Amperes law.
Electrostatic Magnetostatic
( ) ( )
EQF = ( )BuqF ×=
( )zyx ,,ρ ( )zyxJ ,,
Q
204ˆr
rQEπε
= ∫×
=l r
rdlIB 20
4ˆ
πµ
0
encv
vs
QdvdsD ==• ∫∫ ρenc
sl
IdsJdlH =•=• ∫∫D∇ vD ρ=•∇ 0=•∇ B
ED ε= HB µ=dsDE •=∫ψ
2 ρvV∇ JA2∇
dsBB •=∫ψµ
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2
ερvV −=∇ JA 0
2 µ−=∇
Maxwell’s Vortex Model for Displacement Current
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Modern Way to Explain Displacement current by Capacitor Example
Michael Faraday1791-1867
Heinrich Rudolf Hertz1857-1894
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George FitzgeraldOliver Heaviside
Oliver Lodge
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More on the People who influenced today's development
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clat
ure
omen
cod
ern
Nan
d M
oO
ld a
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z
P (X Y Z)Z
Oy
P (X, Y, Z)
Y
X
Rene Descartesx
X
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Rene Descartes
Gauss ρ∇ D
Concluding Overview of Modern Electromagnetic Theory
Divergence / Stokes’s Theorem
vρ=⋅∇ D0=×∇ E
Coulomb’s Law/ Gauss
Law
Define E Faraday’s Law of
Induction t∂∂
−=×∇BE
Biot –Savart
Lorentz Force
Evidence of Special Theory of
RelativityEB ×)/1( 2
Law Ampere’s Circuital Law
Define B Maxwell’s Displacement t∂
∂+=×∇
DJH
EB ×= vc )/1( 2
Gauss Divergence /
Stokes’s
Current concept
JH =×∇
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Stokes s Theorem 0=⋅∇ B
Thank YouThank You
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