Transverse Electromagnetic Waves in Free Space

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

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?

Aim of class today: To derive the EM wave equation

Consider an oscillating electric field Ey x Bz If a charge moves non-uniformly, it radiates z

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

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

Ampere´s law with displacement current term Ey x C/ x z Y By(x) By(x+x)

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

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

Electromagnetic waves for E field for B field

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

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