a mathematical and relativistic approach to Invariance of Maxwell equation.

1. A mathematical approach

2. 
 Masood Karim (lead)
 Shehzad Hussain
 Abdul Hai
 Muhammad Sadiq
 Shams Rehman
 Ghulam Ishaq
Our Team

3. 
Man & the theory
James Clerk Maxwell (1831 – 1879) ,Scottish

4. 
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

5. 

6. Gauss’ Law of Magnetism
The number of line entering a surface is equal to the
number of lines leaving the surface.

7. Divergence
Divergence at a point (x,y,z) is the measure of the vector flow
out of a surface surrounding that point.

8. 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.

9. Also
Electric currents and changes in electric fields are
proportional to the magnetic field circulating about the
area they pierce.

10. 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

11. 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

12. Invariance of Gauss Law
Let us consider

16. Invariance of Ampere’s Law

23. References
A premier of Special relativity by P.L Sardasai
Wikipedia
Hyperphysics
And Us