Question

A plane electromagnetic wave, with wavelength 3.5 m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 440 V/m, oscillates parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time-averaged rate of energy flow associated with this wave? The wave uniformly illuminates a surface of area 2.3 m2. If the surface totally absorbs the wave, what are (g) the rate at which momentum is transferred to the surface and (h) the radiation pressure?

Answer 1

Part (a) : Given wavelength of EM wave ( λ) = 3.5 m

We know that the frequency is related with wavelength as :

Frequency (f) = c/λ = 3×10^8 /3.5 = 8.57 × 10^7 Hz = 85.71 MHz

Frequency = 85.71 MHz

Part(b) : Angular frequency (ω) is given by formula :

ω = 2π*f

Putting values,

ω = 2×3.14 × 8.571 × 10^7 Hz. = 53.83 × 10^7 Hz = 538.28 MHz

Angular frequency (ω) = 538.28 MHz

Part(c) :

Angular wavenumber (k) of a wave is given by formula :

k = 2π/λ

Putting values,

k = 2×3.14/3.5 = 1.79 rad.m^-1

Angular wavenumber is 1.79 rad.m^-1 .

Part(d) :

In an electromagnetic wave the telarelation between Electric field amplitude (E).and magnetic field Amplitude (B) is given by formula :

E/B = c

As Given, Electric field Amplitude(E) = 440 V/m

And we know, c = 3×10^8 m/s

Putting values in above formula,

B= E/c = 440/3×10^8 = 1.134× 10^-6 T = 1.134 μT

Amplitude of magnetic field component (B) = 1.134 μT

Part(e).:

As electric and magnetic field components in and EM wave are perpendicular to each other and also perpendicular to direction of motion.

Given axis of propagation = x axis,

Axis of oscillation of RlecElec field component = Y-axis

So the magnetic field component will oscillate perpendicular to these two axis which is z-axis.