Nature of Electromagnetic Waves and Propagation:
It can be shown from Maxwell’s equations that electric and magnetic fields in an electromagnetic wave are perpendicular to each other and to the direction of propagation. It appears reasonable, say from our discussion of the displacement current. B and E are perpendicular to each other. In figure 17.4, we show a typical example of a plane electromagnetic wave propagating along the X-direction (the fields are shown as a function of the Y-coordinate, at a given time t). The electric field Ey is along the y-axis, and varies sinusoidally with y, at a given time. The magnetic field Bz is along the X-axis, and again, varies sinusoidally with X. The electric and magnetic fields Ex and By are perpendicular to each other, and to the direction Z of propagation. We can write Ey and Bz as follows:
Ey – E0 sin(kx – cωf) …………… (1)
Bz = B0 sin(kx – ωt) ………….. (2)
Here k is related to the wavelength λ of the wave by the usual equation k = 2π/λ and ω is the angular frequency, k is the magnitude of the wave vector (or propagation vector) \(\vec{k}\) and its direction describes the direction of propagation of the wave. The speed of propagation of the wave is (ω / k) using equation (1) and (2) for Ey and Bz and Maxwell’s equation, one finds that
c. = \(\frac{\omega}{k}\) where, c = \(\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\) …………………. (3)
The relation ω = ck is the standard one for waves. This relation is often written in terms of frequency v(= λ/ 2π) and wavelength (λ = 2π/k) as
2πv = \(c\left(\frac{2 \pi}{\lambda}\right)\)
or vλ = c
It is also seen from Maxwell’s equations that the magnitude of the electric and magnetic fields in an electromagnetic wave are related as
B0 = E0/c ………….. (4)
and Em = cBm …………… (5)
If electromagnetic wave propagated in any medium other than vacuum, then speed of light is given by :
\(=\frac{1}{\sqrt{\mu \varepsilon}}=\frac{c}{\sqrt{\mu_{r} \varepsilon_{r}}}\) ……………….. (6)
Where ε is permittivity of the medium and p is the permeability of the magnetic field. εr is relative permittivity and μr. is the relative permeability of the medium. This equation can be written as
v = \(\frac{c}{n}\) ……………. (7)
where, n = \(\sqrt{\mu_{r} \varepsilon_{r}}\) is refractive index of the medium.
Hertz Experiment of Electromagnetic Waves:
The existence of electromagnetic wave was confirmed experimentally by Hertz in 1888. This experiment is based on the fact that an oscillating electric charge radiates electromagnetic waves. The energy of these waves is due to kinetic energy of the oscillating charge.
The experiment arrangement is as shown in figure. It consists of two metal plates A and B placed at a distance of 60 cm from each other. The metal plates are connected to two polished metal spheres S1 and S2 by means of metal rods. Using an induction coil a high potential difference is applied across the small gap between the spheres.
Due to high potential difference across S1 and S2, the air in small gap between the spheres get ionized and provides a path for the discharge of the plates. A spark is produced between S1 and S2 and electromagnetic waves of high frequency radiated.
Hertz was able to produce electromagnetic waves of frequency about 5 × 107 Hz.
Here the plates A and B acts an a capacitor having small capacitance value C and connecting wire provide low inductance L. Thus the plates and the rods (with spheres) constitute an LC combination. The high frequency oscillation of charges between the plates is given by
v = \(\frac{1}{2 \pi \sqrt{L C}}\)
Wavelength of the electromagnetic produced is given by
An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector. This constitutes another LC combination whose frequency can be varied by varying its diameter.
