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

Question

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

a) Evaluate the wavelength lamda.

b) Evaluate w(omega) and k

c) write an 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 x 10^-8 T) determine the amplitude of the electric field .

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

Explanation / Answer

a) lambda = c/f

= 2.998 m

b)

w = 2 pi f = 6.2831*10^8 Hz

k = 2pi /lambda = 2.0957

c)

B = (k X E )/w

where X imply cross product

B = E/c, where B and E are the amplitudes of magnetic field and Electric field

d)

E = 1.0*10^-8 *2.998*10^8 = 2.998

e)

by cross product we get the direction of E to be along -j

so we get

E = 2.998 * cos (2.0957 z - 6.2831*10^8 t) (-j)

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