3. Electromagnetic wave An 200-MHz electromagnetic wave has an magnetic field gi

Question

3. Electromagnetic wave An 200-MHz electromagnetic wave has an magnetic field given by B- B, sin(ky- cot)i, where Bo is 0.020 T. Note that M=106. (a) What are the wavenum berkand angular frequency of the wave? (b) Write down the expression for the electric field. Be sure to compute the magnitude of the electric field and to indicate its direction. (c) Write down the expression for the Poynting vector. Be sure to compute the magnitude of the pointing vector and to indicate its direction. (d) Calculate the force due to radiation pressure if the above wave strikes on a highly (or "perfectly") reflective metallic surface whose area is given by 1.5 m2. 56

Explanation / Answer

Given,

B = 0.02 T ; f = 200 M Hz

a)We know that,

c = f lambda => lambda = c/f

lambda = 3 x 10^8/200 x 10^6 = 1.5 m

We know, k = 2 pi/lambda

k = 2 x 3.14/1.5 = 4.2

Hence, k = 4.2

B)We know that

c = E/B

E = c B = 3 x 10^8 x 0.02 = 6 x 10^6 N/C

w = 2 pi f = 2 x 3.14 x 200 x 10^6 =

E = 6 x 10^6 sin(4.2y - wt) j

c)S = EB/u0

S = 6 x 10^6 x 0.02/4 x 3.14 x 10^-7 = 9.55 x 10^10 W/m^2

since it is perpendicular to both E and B, it is directed along Z.

d)S = P/A

P = S x A

F x d/t = S A

F = S A t/d ;

for unit time and unit distance

F = 9.55 x 10^10 x 1.5 = 1.43 x 10^11 N

Hence, F = 1.43 x 10^11 N

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