For free space p =0

J =0

B =µ0 H

D =ε_{0 }E

Maxwell’s equation for free space.

I div =p

Putting D =ε_{0} E

And P=0

in above equation we getting

div (ε_{0 }E) =0

ε_{0} div E=0

or div E =0

II. div B =0

Putting B =µ _{0 }H

Or div µ_{0 } H =0

µ_{0 } div H =0

div H =0

III . curl E =- Db /dt

Putting B =µ_{0} H in above relation

Curl E =- d (µ_{0} Dh/dt)

IV . curl H =J +Dh /dt

Putting D =ε_{0} E .J =0

Curl H =0+d (ε_{0 }De/dt)

If we take curl of equation (3), we get

Curl (curl E ) = -µ_{0 }d/dt (curl H)

From equation (4), we get

[Gradient (div E ) -∆^{2}E] =- µ

_{0}ε

_{0}d

^{2}E/dt

^{2}

_{ }

From equation (1) div E =0

So the equation (4) become

∆^{2} E =µ _{0} ε_{0} d^{2} E/dt^{2}

^{ }

^{ }E = E_{X}+ E_{Y} +E_{Z}

Then L.H.S is

The wave equation is

D^{2}y/dx^{2}=1/u^{2} (d^{2}y/dt^{2})

where v = velocity of wave

x = path of propagation wave

On comprising the equation (8) and (9), we get

V2 1/µ_{0} ε_{0} and v =1 √µ_{0} ε_{0}

Since a time varying electric field travels in free space with the velocity

v =1 √µ_{0} ε_{0}

for magnetic field

µ_{0} = 4π x 10^{– 7} Henry I farad

ε_{0}= 8.8542 x 10^{-12} Farad/met

v = 2.9999 x 108 met/sec.

Similarly taking curl of equation (4), we getting

curl (curl H) = ε_{0}· d/ dt curl E [From equation (3)]

(grad (div H) =∆2 H ) = – ε_{0} µ_{0} d^{2} H /dt^{2}

H = H_{X} +H_{Y} +H_{Z}

∆^{2} H =µ_{0} ε_{0} d^{2}H /dt^{2}

The wave equation is

D^{2}y/dx^{2} = – 1/u^{2} d^{2}y/dt^{2}

On comprising equations (10) and (11), and taking

µ0 = 4π x 10-7 Henry /met

ε0 = 8.8542 x 10-12 Farad /met

1/ v^{2} =µ_{0} ε_{0}

v=1/√µ_{0} ε_{0} = 2.9999 x 10 8 met / sec