A red light emitted by a laser in a vacuum behaves like a plane wave with a wave

Question

A red light emitted by a laser in a vacuum behaves like a plane wave with a wavelength of 642.6 nm, a beam width of 1 mm, and an amplitude of the electric field oscillations of 400 V/m. What is the frequency of the light? What is the amplitude of the oscillations in the magnetic field? What is the maximum value of the magnitude of the Pointing vector? What is the minimum value of the magnitude of the pointing vector? W/m^2 What is the intensity of the light? W/m^2 What is the average energy per unit volume of the light? nJ/m^3 If we assume that the intensity of the light is constant across the width of the beam and the beam shines on a solar panel with 20% efficiency, what power will the panel supply? mu W What is the momentum of a 1 meter long segment of the beam? times l0^-21kg m/s^2

Explanation / Answer

lambda = 642.6 x 10^-9 m

speed, v = c = 3 x 10^8

frequency = v / lambda = 4.67 x 10^14 Hz ........Ans

Bm = Em / c

= (400 V/m) / (3 x 10^8)

= 1333.33 x 10^-9 T

= 1333.33 nT .....Ans

I_max = Em Bm / u0

= (400) (1333.33 x 10^-9) / (4pi x 10^-7)

= 424.40 W/m^2 ............Ans

Imin = 0 ............Ans

I = Imax / 2 = 212.2 W/m^2 .........Ans

average energy per unit volume = 212.2 / (3 x 10^8)

= 7.07 x 10^-7 J/m^3

= 707 nJ/m^3 .........Ans

Area = pi (1x 10^-3 / 2)^2 = 7.85 x 10^-7 m^2

Power = intensity x area

= (212.2) (7.85 x 10^-7)

= 166.67 x 10^-6 W

= 166.67 uW .........Ans

energy of 1 meter segment , E = (7.07 x 10^-7) ( 7.85 x 10^-7 x 1)

= 5.55 x 10^-13 J

p = E / c = 1.85 x 10^-21 kg m / s^2

Ans: 1.85

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