1. Transverse Electromagnetic Waves in Free Space

2. “Let there be electricity and magnetism
and there is light”
J.C. Maxwell

3. What we know from previous classes?
Oscillating magnetic field generates electric field (Faraday´s law) and vice-versa (modified Ampere´s Law).
Reciprocal production of electric and magnetic fields leads to the propogation of EM waves with the speed of light.
Question: WAVES?????? How do we show that a wave is obtained?

4. Aim of class today: To derive the EM wave equation

5. Consider an oscillating electric field Eyx Bz
If a charge moves non-uniformly, it radiates z

6. Y
This will generate a magnetic field along the z-axis
Ey(x+x)
Ey(x) C x Z
We know that Faraday´s law in the integral form in given as:
where C is the rectangle in the XY plane of length l width x, and S is the open surface spanning the contour C

7. Faraday´s law on the contour C
this implies...
Keep this is mind...

8. Ampere´s law with displacement current termEy x C/ x z Y
By(x)
By(x+x)

9. Ampere´s law, for the Contour C/
this implies...

10. Using the eq. obtained earlier i.e.,
The EM wave equation
Note: Similar Equation can be derived for Bz

11. Electromagnetic waves
for E field
for B field

12. In general,
electromagnetic waves
Where  represents E or B
or their components

13. Reference 1. FEYNMAN LECTURES ON PHYSICS VOL I
Author : RICHARD P FEYNMAN,
IIT KGP Central Library
Class no.  530.4
2. OPTICS
Author: EUGENE HECHT
Class no. 535/Hec/O