Consider that an electromagnetic wave be travelling along +ve X-direction. The electric field is along Y-axis and magnetic field along Z-axis as shown in Fig.
Let at any time t. the wave be in plane KLMN and at time t + dt, it advances to plane PQRS.
If c is the velocity of e.m. wave, then the distance covered by the wavefront in time dt is given by KP = LQ = MR = NS = c dt
As the wavefront propagates, there is change in magnetic flux through the face BCGF and electric flux changes through face ABFE
(i) Change in magnetic flux through face BCGF
Increase in magnetic flux
dΦB = B x Increase in area
= B [LM x LQ]
= B dy c dt
or \(\frac{d\phi _B}{dt}\) = B c dy
From Farady's law pf electromagnetic induction, we have
i.e. ratio of electric and magnetic field is equal to velocity of light.
(ii) Change in electric flux through face ABFE
Increase in electric flux
dΦe = E(Increase in area)
or dΦe = E [PQ x LQ]
= E dz c dt
or \(\frac{d\phi _e}{dt}\) = c E dz .........(4)
Ampere's law in the absence of conduction current is given by
\(\oint_{ABFEA} \overrightarrow E . \overrightarrow {dl} = \mu_0\varepsilon_0 \frac{d\phi_e}{dt}\) [∵ I = 0]
By using the same technique as used in solving,
This is speed of light in free space. Thus we find that light is e.m.wave.
In a material medium, the velocity of e.m.wave is given by
C = \(\frac{1}{\sqrt {\mu\varepsilon}}\)
where µ and ε be permeability and permittivity of the medium.
