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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