meaning for modern electrical engineering«Consideration Concerning the Fundamental of Theoretical...
Transcript of meaning for modern electrical engineering«Consideration Concerning the Fundamental of Theoretical...
Maxwell’s Equations and their
meaning for modern electrical
engineering:
How humans can deal with things they cannot see
Bjarte Hoff
PhD Candidate
Institute of Electrotechnology
UiT The Arctic University of Norway
Maxwell’s equations
0
0 0
(Gauss's law)
0 (Gauss's law for magnetism)
(Ampere's law)
(Faraday's law)
encl
EC
encl
B
Qd
d
dd i
dt
dd
dt
E A
B A
B l
E l
є
є
1749 -> 1854
André-Marie Ampére (1775-1836)Hans Christian Ørsted (1777-1851)
Electric currents createmagnetic fields
Laid the fundation of«Electrodynamics»
Ampéres law
1749 -> 1854
Michael Faraday (1791-1867)Georg Simon Ohm (1789-1854)
Ohm’s law Electromagnetism, electrochemistry,
induction
1749 -> 1854
James Clerk Maxell (1831-1879)William Thomson (1824-1907)Lord Kelvin
ElectricityThermodynamics
Electromagnetic wavesMaxwell’s equations
Maxwell’s work – The beginning
In a letter to William Thomson in 1854:
“Suppose a man to have a popular knowledge of electrical show and little antipathy to Murphy’s Electricity, how ought he to proceed in
reading and working so as to get an little inside into the subject which may be of use in future reading?
If he wish to read Ampere, Faraday, et cetera, how should they be arranged and at what stage and in what order might he read your
articles in the Cambridge journal?”
Maxwell’s 1st paper:
«On Faradays Lines of Force»
Maxwell:
«By referring everything to the purely geometrical idea of the motion of an imaginary
fluid, I hope to attain generality and precision, and to avoid the dangers arising from a
premature theory professing to explain the cause of the phenomena»
Faraday’s Lines of Force -> Tubes of Force
Incompressible fluid used as an analogy
Maxwell’s 2nd paper:
«On Physical Lines of Force»
Maxwell:
«I propose now to examine magnetic phenomena from a mechanical point of view,
and to determine what tensions in, or motions of, a medium are capable of producing
the mechanical phenomena observed»
Mechanical bipolar molecular vorticies (or eddies) seperated by a layer ofparticles are used as an analogy.
Maxwell’s 2nd paper:
«On Physical Lines of Force»
Maxwell:
«I propose now to examine magnetic phenomena from a mechanical point of view,
and to determine what tensions in, or motions of, a medium are capable of producing
the mechanical phenomena observed»
Mechanical bipolar molecular vorticies (or eddies) seperated by a layer ofparticles are used as an analogy.
“We have thus obtained a point of view from which we may regard the relation of an electric current to its line of force as analogous to the relation of a toothed wheel or rack to wheels which it drives.”
Maxwell’s 2nd paper:
«On Physical Lines of Force»
Maxwell:
«I propose now to examine magnetic phenomena from a mechanical point of view,
and to determine what tensions in, or motions of, a medium are capable of producing
the mechanical phenomena observed»
Mechanical bipolar molecular vorticies (or eddies) seperated by a layer ofparticles are used as an analogy.
“We have thus obtained a point of view from which we may regard the relation of an electric current to its line of force as analogous to the relation of a toothed wheel or rack to wheels which it drives.”
“The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. I do not bring it forward as a mode of connexion existing in nature, or even as that I would willingly assent to as an electrical hypothesis.”
Maxwell’s 3rd paper:
«A Dynamic Theory of the Electromagnetic Field»
Reformulated into a electromagnetic theory, without any sort of mechanical analogy
• Part III lists Maxwell’s original 20 equations for the electromagnetic field:
Three equations of:
- Magnetic Force
- Electric Currents
- Electromotive Force
- Electric Elasticity
- Electric Resistance
- Total Currents
• Part VI contains electromagnetic theory of light
«We now proceed to investigate whether these properties of that which constitutes the electromagnetic field, deduced from electromagnetic phenomena alone, are sufficient to explain the propagation of light through the same substance.»
One equation of:
- Free Electricity
- Continuity
From 1865 to today
1865 Maxwell publish his 20 equations and 20 variables in:«A Dynamical Theory of the Electromagnetic Field»
1884 Heinrich Hertz publish his derivation of Maxwell’s Equations:«On the Relations between Maxwell’s Fundamental Electromagnetic Equations and the Fundamental Equations of the Opposing Electromagnetics»
1885-1887 Oliver Heaviside reformulated 12 of Maxwell’s 20 equations into 4:Several papers: Electrical Papers, vol. 1 and 2, London, UK: MacMillan and Co., 1892.
1940 Albert Einstein referred to Maxwells equations in:«Consideration Concerning the Fundamental of Theoretical Physics»
1873 Maxwell correct a sign error and include more equations in:«A Treatise on Electricity and Magnetism»
From 1865 to today
1865 Maxwell publish his 20 equations and 20 variables in:«A Dynamical Theory of the Electromagnetic Field»
1884 Heinrich Hertz publish his derivation of Maxwell’s Equations:«On the Relations between Maxwell’s Fundamental Electromagnetic Equations and the Fundamental Equations of the Opposing Electromagnetics»
1885-1887 Oliver Heaviside reformulated 12 of Maxwell’s 20 equations into 4:Several papers: Electrical Papers, vol. 1 and 2, London, UK: MacMillan and Co., 1892.
1940 Albert Einstein referred to Maxwells equations in:«Consideration Concerning the Fundamental of Theoretical Physics»
1873 Maxwell correct a sign error and include more equations in:«A Treatise on Electricity and Magnetism» «The so-called special or restricted relativity theory is based on the fact that Maxwell’s equations (and thus the law of propagation of light in space) are converted into equations of the same form, when they undergo Lorentz transformation.»A. Einstein, 1940
Maxwell’s equations today
0
0 0
(Gauss's law)
0 (Gauss's law for magnetism)
(Faraday's law)
(Ampere's law)
encl
B
EC
encl
Qd
d
dd
dt
dd i
dt
E A
B A
E l
B l
Gauss’s law for electric fields
+
E
q
0
enclE
Qd
E A
0
q
Total flux through any closed surface,is proportional to the total charge insidethe surface:
12
0 8.8541.. 10 - Permittivity in vacuumF m
0
0
A
B
C
D
Q q
Q q
Q
Q
Gauss’s law for magnetism
0B d B A
Total magnetic flux through any closedsurface, is always zero (no monopoles):
N
S
B
A magnet will always have twopoles, hence total flux is zero.
Faraday’s law
Bdd
dt
E l
A changing magnetic field is accompanied by a changingelectric field at right angles to the change of the magneticfield
B
Bdl
EMF
B
E
E
EE
E
E
Changing magnetic flux resultsin a electric field and therebya current around the loop:
i
i
1[ ] [ ] [ ]E d E Vm l m V V l
Ampere’s law
0 0E
C
encl
dd i
dt
B l
An electric current is accompanied by a magneticfield whose direction is at right angles to the current flow B
B
B
B
Ci
B
Ci
Ampere’s law – Maxwell’s extension
0 0E
C
encl
dd i
dt
B l
B ?B
Q Q
Time-varyingelectric field
Maxwell extension:A changing electric field is accompanied by a changingmagnetic field
Displacement current
Capacitor
Battery
Electromagnetic waves
0 0E
C
encl
dd i
dt
B l
Ampere’s law - Maxwell extension:A changing electric field is accompanied by a changing magnetic field
Bdd
dt
E l
Faraday’s law:A changing magnetic field is accompaniedby a changing electric field
0 0 2
1µ
c
Faraday’s law and Ampere’s law - Transformer
Alternating current(50 Hz)
Changing electric flux Bd
dt
Ideal magnetic core material
Alternating current(50 Hz)
Bdd EMF
dt
E l
0 Cd i B l
Ampere’s law:Faraday’s law:
B
Maxwell’s Equations today?
Robert «Bob» Scully, former President IEEE EMC Society:
«Truly, Maxwell’s Equations are the heart and soul of our discipline»
Maxwell’s Equations and Electrical Engineers
0
0 0
(Gauss's law)
0 (Gauss's law for magnetism)
(Faraday's law)
(Ampere's law)
encl
B
EC
encl
Qd
d
dd
dt
dd i
dt
E A
B A
E l
B l
Bibliography
• J. C. Maxwell, «On Physical Lines of Force, part 1-4,» London-Edinburgh-Dublin Philosph. Soc., vol. 21-23, 1861-1862.
• J. C. Maxwell, «A Dynamical Theory of the Electromagnetic Field,» in Philosophical Transactions of the Royal Society of London, UK, 1865, pp. 459-512.
• A. Einstein, «Consideration Concerning the Fundaments of Theoretical Physics,» Science, New Series, vol. 19, No. 2369, The Science Press, New York, NY, 24 May 1940, pp. 487-492.
• J. C. Maxwell, The scientific papers of James Clerk Maxwell, New York: Dover Publications, 1965.
• H.D. Young and R. A. Freedman, University Physics, 11th ed. Texas: Pearson, 2004.
• D. Fleisch, A Student’s Guide to Maxwell’s Equations, Cambridge University Press, UK, 2008.
• R. Scully, «The Evolution of Maxwell’s Equations Through a Brief Critical Examination of the History and Background of the Man and His Times – Part 1-4,» IEEE Electromagnetic Compatibility Magazine 2013-2014.
• R. Scully, «Maxwell’s Legacy: The Heart and Soul of the EM Discipline,» IEEE MTT-S International Microwave Symposium, Phoenix, AZ, 2015.
• D. Brooks, Maxwell’s Equations Without The Calculus, Kirkland, 2016.