is the same dynamical theory of electromagnetic fields ... fileis the same dynamical theory of...
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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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