The oscillating magnetic field in a plane electromagnetic wave is given by
B_y = (8 × 10^-6) sin [2 × 10¹¹ t + 300 $π$ x] T
(i) Calculate the wavelength of the electromagnetic wave.
(ii) Write down the expression for the oscillating electric field.

Solution

Given equation for oscillating magnetic field is,
B_y = (8 × 10^-6) sin [2 × 10¹¹ t + 300

π

x]T .

Comparing the given equation with the equation of magnetic field varying sinusoidally with x and t

B_{y} = B_{0} \sin (\frac{2 π x}{λ} + \frac{2 π t}{T})

we get,

\frac{2 π}{λ} = 300 π

∴

λ = \frac{2}{300} = 0.0067 m

and

B_{0} = 8 \times 10^{- 6} T

(i) Wavelength of the electromagnetic wave,

λ = 0.0067 m

(ii) Magnitude of electric field is calculated by,

E_{0} = {CB}_{0} = 3 \times 10^{8} \times 8 \times 10^{- 6}

= 24 \times 10^{2} = 2400 {Vm}^{- 1}

∴

The required expression for the oscillating electric field is,

E_{z} = E_{0} \sin (\frac{2 π x}{λ} + \frac{2 π t}{T}) = 2400 \sin (300 π x + 2 \times 10^{11} t) V / m .

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