Q. 84.0( 12 Votes )
Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B0, ω, k, and λ. (b) Find expressions for E and B.
Answer :
Given: Electric field amplitude of electromagnetic wave, E0 = 120 N/C
Frequency of electromagnetic wave, v = 50 MHz
(a) Magnitude of magnetic field is given by the following expression:
B0 = E0/c
⇒ B0 = 40 × 10-8 T
Converting it into nT, we get B0 = 400 nT
Angular frequency can be calculated as follows:
ω = 2πv
where ν is the linear frequency.
ω = 2×3.14×50×106Hz
ω = 314 × 106 rad/s
ω = 3.14 × 108 rad/s
Propagation constant k is given by the following expression:
k = ω /c
K = 1.05 rad/m
Wavelength can be calculated by the following expression:
λ = c/v
⇒ λ = 6 m
(b) The expression for electric field and magnetic field can be written as follows:
Let a wave is propagating in positive x- direction.
Since all the three vectors are mutually perpendicular to each other. The electric field vector will be in positive y- direction and magnetic field vector will be in positive z-direction.
Electric field vector can be expressed in the form of equation as given below:
⇒
Substituting values in above equation we get
Magnetic field vector can be expressed in form of following equation:
⇒
Substituting values in above equation we get
⇒
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