Transcript
Invariance of Maxwell’s equation
A mathematical approach
Masood Karim (lead) Shehzad Hussain Abdul Hai Muhammad Sadiq Shams Rehman Ghulam Ishaq
Our Team
Man & the theory
James Clerk Maxwell (1831 – 1879) ,Scottish
What is it all about..?
The Maxwell’s Equations are a description of classical electric and magnetic fields in presence or absence of sources Guass’s Law
Guass Law for Magnetism
Faraday’s Law
Ampere’s Law
Gauss’ Law of Magnetism The number of line entering a surface is equal to the number of lines leaving the surface.
DivergenceDivergence at a point (x,y,z) is the measure of the vector flow out of a surface surrounding that point.
Ampere’s Law
For any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.
AlsoElectric currents and changes in electric fields are proportional to the magnetic field circulating about the area they pierce.
Invariance/Invariants
The quantities whose values don’t change in any transformation are called Invariants.
Example of a physical invariant is the speed of light under a Lorentz transformation.
Time under a Galilean transformation
How we figure out...Invariance of Maxwell’s equation?
Show that a spherical light wave spreads uniformly with velocity c in all inertial frame.
The Lorentz Invariance means that the amplitude should be symmetric under translations of space and time and rotations. In the wave eq. you have only 2nd derivatives (time and space), hence symmetry under Lorentz is preserved
Invariance of Gauss LawLet us consider
Invariance of Ampere’s Law
References
A premier of Special relativity by P.L Sardasai
Wikipedia
Hyperphysics
And Us
top related