Question

Let an electromagnetic wave propagate along the x-direction, the magnetic field oscillates at a frequency of 10¹⁰ Hz and has an amplitude of 10^-5 T, acting along the y – direction. Then, compute the wavelength of the wave. Also write down the expression for the electric field in this case.

Answer 1

Frequency of electromagnetic wave, v = 10¹⁰ Hz

Amplitude of Oscillating magnetic field, B₀ = 10^-5 T

Wave length of the wave, λ = `"C"/"f" = (3 xx 10^8)/10^10 = 3 xx 10^-2`m

Amplitude of oscillating electric field, E₀ = B₀ C

C = `"E"_0/"B"_0`

E₀ = 10^-5 × 3 × 10⁸

E₀ = 3 × 10³ = NC^-1

Experession for the electric field in Oscillating wave

E = E₀ sin (kx -wt)

K = `(2pi)/lambda = (2 xx 3.14)/(3 xx 10^-2) = 209 xx 10^2`

W = 2πƒ = 2 × 3.14 x 10¹⁰ = 6.28 × 10¹⁰

`vec"E"`  = 3 x 10³ sin (2.09 × 10² x – 6.28 × 10¹⁰ t) `hat"i"` NC^-1.