Question

4. (8 Points) An electromagnetic wave, with a frequency of f-100 MHz, is traveling through vacuum in a direction we can call the x-axis. At t = 0, the electric field due to this wave at x = 0 has a magnitude of 300 V/m. a. Determine the wavelength of this wave. b. If this wave entered your eye would you see anything; explain why or why not. What region of the electromagnetic spectrum does this wave occupy? e. Determine the magnitude of the magnetic field at the instant t O d. How much time passes after t 0 before the electric and magnetie fields at x-0 are exactly the same amplitude as they were at tm0

Answer 1

For waves we have a relation E = hV E = hc/lambda by these two hV = hc/lambda lambda = c/V E = Energy lambda = wavelength h = planks constant V = frequency = 100 MHz C = speed of light = 3 times 10^8 ms^-1 lambda = 3 times 10^8 ms^-1/100 times 10^-6 S^-1 = 3m wavelength = 3m Ans b) As wavelength is 3m we can't see it human eye visible light has wavelength 4 times 10^-6 m to 7 times 10^-6 m. wave will not be visible to humans This wavelength falls in radio wave region of electromagnetic spectrum c) We know that squareroot of ratio of electric field to that of magnetic field is equal to speed of light squareroot E_0/B_0 = C E_0 = magnitude of electric field B_0 = magnitude of magnetic field E_0 = 300 B_0 = c^2/E_0 B_0 = (3 times 10^8)/300 = 3 times 10^14 T Ans