2) An electromagnetic wave traveling in a vacuum has an electric field given by:

Question

2) An electromagnetic wave traveling in a vacuum has an electric field given by: ?(x,t)-(3.50 x 104 V-n)sin!(2.51 x 105 rad/n): +or!} What is the speed of this wave? What is the amplitude of the magnetic component? What is the wavelength of this wave? What is the frequency [in Hz] of this wave? In which direction is the wave traveling? ( j -k +k) If you assume that the equation above represents planar EM waves that are incident upon a perfectly absorbing sphere of radius 0.25m, and mass 0.15kg, how much energy does the sphere absorb from the EM waves in 30s? U- If the above sphere was stationary at t 0, how fast is it moving att 30s?

Explanation / Answer

2. E = E_max sin[ k x + w t ]

Speed = c = 3 x 10^8 m/s .....Ans

Bm = Em / c = (3.50 x10^4)/(3 x 10^8)

Bm = 1.17 x 10^-4 T .....Ans

  
k = 2 pi / wavelength = 2.51 x 10^5

wavelength = 2.50 x 10^-5 m .......Ans

f = v / wavelength = 1.2 x 10^13 Hz .....Ans

direction -> along -i  

I = Em Bm / (2 u0)

I = (1.17 x 10^-4 x 3.50 x 10^4) / (2 x 4pi x 10^-7)

I = 1.625 x 10^6 W/m^2

P_absorbed = I A = (I)(pi R^2)

= 319000 W

U = P t = 9.57 x 10^6 J ....Ans

U = m v^2 /2

v = 11300 m/s ...Ans

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