8.8 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.

(a)
Hint: \(c=\frac{E_{0}}{B_{0}}\)
Step 1: Magnitude of magnetic field strength.

B0=E0c=1203×108=4×10-7 T=400 nT

Step 2: Find the angular frequency of the source.

Step 3: Find the propagation constant.

k=ωc=3.14×1083×108=1.05 rad/m

Step 4: Find the wavelength.

λ=cν=3×10850×106= 6.0 m

(b)
Hint: Electric field vector and the magnetic field vector are mutually perpendicular.
Step 1: Identify the direction of electric field vector and magnetic field vector.
If the wave is propagating in the positive x-direction, the electric field vector will be in the positive y-direction and the magnetic field vector will be in the positive z-direction.
Step 2: Find the Equation of electric field vector.

Equation of electric field vector is given by:

E=E0sin(kx-ωt)j^=120sin1.05x-3.14×108tj^



Step 3: Find the Equation of magnetic field vector.
\(\vec{B}=B_{0}~sin\left ( kx-\omega t \right )\hat{k}\)
\(\vec{B}=\left ( 4 \right )\times 10^{-7}~sin\left [ 1.05x-3.14\times 10^{8}t \right ]\hat{k}\)