In SI units, the electric field in an electromagnetic wave is described by E_ y

Question

In SI units, the electric field in an electromagnetic wave is described by E_ y = 102 sin(1.40 times 10^7 x - omega t). (a) Find the amplitude of the corresponding magnetic field oscillations. mu T (b) Find the wavelength lambda. mu m (c) Find the frequency f. Hz What is the average magnitude of the Poynting vector 4.00 mi from a radio transmitter broadcasting isotropically (equally in all directions) with an average power of 220 kW? mu W/m^2 The human eye is very sensitive to light having a wavelength of 5.46 times 10^-7 m, which is in the green-yellow region of the visible electromagnetic spectrum. What is the frequency of this light? Hz Plane-polarized light is incident on a single polarizing disk with the direction of x_0 parallel to the direction of the transmission axis. Through what angle should the disk be rotated so that the intensity in the transmitted beam is reduced by a factor of: (a) 2.00 degree (b) 6.20 degree (c) 14.0 degree

Explanation / Answer

1) a)

B = E/c

= 102/3.0*108 m/s

= 34*10-8 T

=0.34*10-6 T = 0.34 T

b)

k = 1.40*107,

wavelength = 2/k

= 2*3.14/1.40*107

= 4.49*10-7 m = 0.449m

c)

f = c/

= 3.0*108 m/s / 4.49*10-7 m

= 6.68*1014 Hz

2)

1 mile = 1609.34 meter

4.00 mile = 6437.36 meter

S = I/A = I/4R2 = 220*103/(4*3.14*(6437.36)2) = 423 µW/m2

3)

wavelenght = 5.46*10-7

wavelenght*frequency = c = 3*108

Frequency = (3*108 )/(5.46*10-7) = 5.49*1014 Hz

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