Question

Electromagnetic Waves 2 1 2 3 45 6 A plane monochromatic electromagnetic wave with wavelength ? field is described by 2.6 cm, propagates through a vacuum. Its magnetic where B, -2.7 x 106 T, By-3 x 06 T, and i-hat and j-hat are the unit vectors in the x and y directions, respectively. 1) What is f, the frequency of this wave? GHZ Submit You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is I, the intensity of this wave? W/m2 Submit You currently have O submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is Sz, the z-component of the Poynting vector a-0, y 0, z 0? W/m2 Submit You currently have O submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question. 4) What is Ex, the x-component of the electric field at (x-0, y 0, z-0) at t0? V/m Submit You currently have O submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question.

Answer 1

Given,

lambda = 2.6 cm = 0.026 m

Bx = 2.7 x 10^-6 T ; By = 3 x 10^-6 T

1)We know that

v = f lambda

f = v/lambda

f = 3 x 10^8/0.026 = 1.154 x 10^10 Hz

Hence, f = 11.54 x 10^9 Hz = 11.54 gHz

b)B = sqrt (Bx^2 + By^2)

B = sqrt (2.7^2 + 3^2) x 10^-6 = 4.04 x 10^-6 T

S = c B^2/2 u0

S = 3 x 10^8 x (4.04 x 10^-6)^2/( 2 x 4 x 3.14 x 10^-7) = 1949.24 W/m^2

Hence, S = 1949.24 W/m^2

c)Sz = c Bz/2 u0

Sz = 2 S = 2 x 1949.24 = 3898.48 W/m^2

Hence, Sz = 3898.48 W/m^2

d)Ex = c By

Ex = 3 x 10^8 x 3 x 10^-6 = 900 W/m^2

Hence, Ex = 900 W/m^2