The electric field of an electromagnetic wave traveling in a vacuum is described

Question

The electric field of an electromagnetic wave traveling in a vacuum is described by the equation E = (6.10 103)sin(kz t) V/m, where the electric field oscillates along the y direction.

(a) In what direction is this wave traveling?

(b) If the wavelength is 490 nm, what is the frequency, angular frequency, and wave number for this wave? (Hz) (rad/s) (rad/m)

(c) Along which direction does the associated magnetic field oscillate?

(d) Write an equation describing the associated magnetic field as a function of z and t. (Do not use other variables, substitute numerical values. Assume that B is in teslas, z is in meters, and t is in seconds. Do not include units in your answer.) B(z, t) =

Explanation / Answer

Here ,

a) the direction of propagation of wave is + Z direction

b)

frequency = 3 *10^8/(490 *10^-9) = 6.122 *10^14 hZ

angular frequency = 2pi * 6.122 *10^14 = 3.846 *10^15 rad/s

wavenumber = 2pi/(490 *10^-9) = 1.28 *10^7 rad/m

c)

as S = E X H

z = j X H

H = - i

hence , the magnetic field is in negative x direction

d)

Now , for the magnetic field

B = (6.10 10^3/(3 *10^8))sin(kz t)

B = 2.033 *10^-11 * sin(1.28 *10^7 * Z - 3.846 *10^15 * t )

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