In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of `2.0 xx 10^(10) 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 xx 10^(8) m s^(-1).]`

Explanation

Energy density in the electric field,
`rho_(E )=(1)/(2)in_(0)E_(rms)^(2)`
Energy density in the magnetic field,
`rho_(B)=(1)/(2)(B_(rms)^(2))/(mu_(0))`
`rArr (rho_(E ))/(rho_(B))=((E_(rms))/(B_(rms)))^(2)xx in_(0)mu_(0)`
`= c^(2)xx(1)/(c^(2)) because c=(1)/(sqrt(in_(0)mu_(0)))rArr c^(2)=(1)/(in_(0)mu_(0))`
= 1
`rArr rho_(E )= rho_(B)`