The B-field of a plane electromagnetic plane wave is given, using complex notati

Question

The B-field of a plane electromagnetic plane wave is given, using complex notation, as B = 1.50(10^-10)T exp{j[1.8752(10^7)x + 5.6068(10^15)t]} In this expression "j" = Squareroot (-1). The tilde (~) over the B simply indicates that B is a complex function. The "T" stands for Tesla, and all other numbers carry standard SI units. Show your work in calculating the following: (a) the wavelength (b) the period (c) the wave speed and direction of travel (d) the amplitude of the electric field (e) the plane of oscillation of B, assuming that E oscillates in the x-y plane.

Explanation / Answer

The magnetic field is in form of :

B = B_0 exp(kx + omega t)

Here B_0 = 1.50*10^-10 T

k = 1.8752*10^7 m^-1

omega = 5.6068*10^15 rad/s

a)

wavelength = 2pi/k = 2pi/(1.8752*10^7) = 3.35067476*10^-7 m= 335.067 nm

b)

The time period = 2pi/omega = 2pi/( 5.6068*10^15) = 1.1206366*10^-15 sec

c)

The wave speed = omega/k = (5.6068*10^15)/(1.8752*10^7 ) = 298997440 m/s

d)

The electric field amplitude = c times amplitude of magnetic field = 3*10^8*1.50*10^-10 = 0.045 V/m

e)

E and B are perpendicular to each other. Since electric field is in xy plane then magnetic field will be in y-z or x-z plane.

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