Energy in Electromagnetic Waves Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light calong the x axis through vacuum. Its electric and magnetic field vectors are as follows E=E0 sin (ka -wt)3. B = B0 sin (kx-wt) k Throughout, use these variables (E, B, Eo, Bo, k, x, and w) in your answers. You will also need the permittivity of free space eo and the permeability of free space 140 Note: To indicate the square of a trigonometric function in your answer, use the notation sin(x)A2 NOT sinA2(x)

Instantaneous Energy Electric Field = ue(t)= ε₀(E₀*sin(kx-wt))²/2

Instantaneous Energy Magnetic Field = ub(t)= B₀(E₀*sin(kx-wt))²/2μ₀

Average Energy Density  of electric field of the wave = E₀² ε₀/4

Average Energy Density  of Magnetic field of the wave <ub>= B₀²/4μ₀

The Poynting Vector = S = ε₀*c*E₀²/2x

Explanation:  The relationship between μ₀ and ε₀ is

                                                  μ₀= 1/ε₀c²

To Poynting flux definition is provided in the image.

Average Density of the whole wave could then be found by:

                                         <u> =(E₀² ε₀/4)+ (B₀²/4μ₀)

To get to a better answer you can subsitute the relationship between μ₀ and ε₀

Remember: c = the speed of light in vacuum = 3.0 * 10⁸ m/s                    

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day