In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 1010 Hz and amplitude 48 V m−1.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the B field. [c = 3 × 108 m s−1.]
Frequency of the electromagnetic wave, ν = 2.0 × 1010 Hz
Electric field amplitude, E0 = 48 V m−1
Speed of light, c = 3 × 108 m/s
(a) Wavelength of a wave is given as:
(b) Magnetic field strength is given as:
(c) Energy density of the electric field is given as:
And, energy density of the magnetic field is given as:
∈0 = Permittivity of free space
μ0 = Permeability of free space
We have the relation connecting E and B as:
E = cB … (1)
`c=1/(sqrt(in_0mu_0))` … (2)
Putting equation (2) in equation (1), we get
Squaring both sides, we get