An electromagnetic wave propagating in the z-direction at 2.998*10^8 m/s has a f

Question

An electromagnetic wave propagating in the z-direction at 2.998*10^8 m/s has a frequency of f = 100*10^6 Hz. The wave's magnetic field B(z,t) = (1.0*10^-8 T)cos(kz-omega*t)i, where the angular frequency omega = 2*pi*f and the wave number k = 2*pi/lamda

a) Evaluate the wavelength lamda

b)Evaluate omega and k

c) Write the equation that relates the magnetic field B, the electric field E and the speed c for an electromagnetic plane wave

d) Using the relation from c) and the amplitude of the magnetic field B = (1.0*10^-8 T), determine the amplitude of the electric field

e) using the values found in a) and d), write the expression for the electric field E(z,t) for this wave.

Explanation / Answer

a. as V= Lf

wavelength L = V/f = 3e8/100*10^86 = 3 m

b. wave no. k = 2pi/L = 2*31.4/3 = 2.0933 /m

w = 2pif = 2*3.14* 10^8 = 6.28*10^8

c. EF E and Mag field B are related as E = Bc

where cis velocity of light

d. E = 1*10^-8 * 3*10^8 = 3 N/C or V/m

e. E = E0 cos (kz-wt)

E = 3 * cos (2.09z-6.28*10^8 t)

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