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