34: Enhanced EOC: Problem 34.14

INTRO:
The magnetic field of an electromagnetic wave in a vacuum is B_z=(2.0μT)sin((9.00×10⁶)x−ωt), where x is in m and t is in s.

Part A:
What is the wave's wavelength?
Express your answer to three significant figures and include the appropriate units.

SOLUTION:
a value for k is given in the formula
k=9.00×10⁶
since λ=2π⋅1/k, 
λ = 2π⋅1/9.00×10⁶ = 6.98×10^-7 m= 698 nm

Part B:
What is the wave's frequency?
Express your answer to three significant figures and include the appropriate units.

SOLUTION:
using the formula c=fλ, we can easily solve for frequency 
f = c/λ = 3.0×10⁸m / 6.98×10^-7 m⋅s
f = 4.3×10¹⁴ Hz

Part C:
What is the wave's electric field amplitude?
Express your answer to two significant figures and include the appropriate units.

SOLUTION:
E₀=cB₀
→c(2.0μT) 
E₀ = 599.6 N/C ≈ 600 V/m