Question 7 of 8intermediate🔧 ApplyNumerical3 marks

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)
Answer

B₀ = 400 nT (or 4×104 \times 10⁻⁷ T), ω = π × 10⁸ rad/s, k = π/3 rad/m, λ = 6 m

(b)
Answer

E = 120 sin[(π/3)z - (π × 10⁸)t] N/C, B = 4×104 \times 10⁻⁷ sin[(π/3)z - (π × 10⁸)t] T

Explanation

This question tests the relationship between electric and magnetic field amplitudes in electromagnetic waves, and the basic wave parameters. The key formulas from the textbook are: B₀ = E₀/c (relating field amplitudes), ω = 2πν (angular frequency), νλ = c (relating frequency and wavelength), and ω = ck (relating angular frequency and wave number). The sinusoidal expressions follow the standard form given in the text for waves propagating along the z-direction.