Q. 84.0( 12 Votes )

# Suppose that the electric field amplitude of an electromagnetic wave is E_{0} = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B_{0}, ω, k, and λ. (b) Find expressions for E and B.

Answer :

Given: Electric field amplitude of electromagnetic wave, E_{0} = 120 N/C

Frequency of electromagnetic wave, v = 50 MHz

(a) Magnitude of magnetic field is given by the following expression:

B_{0} = E_{0}/c

⇒ B_{0} = 40 × 10^{-8} T

Converting it into nT, we get B_{0} = 400 nT

Angular frequency can be calculated as follows:

ω = 2πv

where ν is the linear frequency.

ω = 2×3.14×50×10^{6}Hz

ω = 314 × 10^{6} rad/s

ω = 3.14 × 10^{8} 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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