Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in...

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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 c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: Ē Eo sin(kx - wt), = B = Bo sin (kr – 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 and the permeability of free space μo. Note: To indicate the square of a trigonometric function in your answer, use the notation sin (x)^2 NOT sin^2 (x). What is the instantaneous energy density ug (t) in the electric field of the wave? Give your answer in terms of some or all of the variables in E=E sin (kr - wt). ▸ View Available Hint(s) IVE ΑΣΦ ug (t) = Submit Part B ug (t) = What is the instantaneous energy density ug (t) in the magnetic field of the wave? Give your answer in terms of some or all of the variables in B = Besin (kz-wt). View Available Hint(s) IVE ΑΣΦ Submit 1 Part C ? 1 ? What is the average energy density (ug) in the electric field of the wave? Give your answer in terms of € and Eo. What is the average energy density (ug) in the magnetic field of the wave? Give your answer in terms of μ and Bo. ▸ View Available Hint(s) (up) = Submit Part E IVE ΑΣΦ From the previous results, derive an expression for (u), the average energy density in the whole wave. Express the average energy density in terms of En and Eg only. The Poynting vector 5 gives the energy flux per unit area of electromagnetic waves. It is defined by the relation S- EXB Ho Calculate the time-averaged Poynting vector (S) of the wave considered in this problem. Give your answer in terms of Eg, c and ep and unit vectors i, j, and/or k. Do not use μ or Bg. 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 c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: Ē Eo sin(kx - wt), = B = Bo sin (kr – 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 and the permeability of free space μo. Note: To indicate the square of a trigonometric function in your answer, use the notation sin (x)^2 NOT sin^2 (x). What is the instantaneous energy density ug (t) in the electric field of the wave? Give your answer in terms of some or all of the variables in E=E sin (kr - wt). ▸ View Available Hint(s) IVE ΑΣΦ ug (t) = Submit Part B ug (t) = What is the instantaneous energy density ug (t) in the magnetic field of the wave? Give your answer in terms of some or all of the variables in B = Besin (kz-wt). View Available Hint(s) IVE ΑΣΦ Submit 1 Part C ? 1 ? What is the average energy density (ug) in the electric field of the wave? Give your answer in terms of € and Eo. What is the average energy density (ug) in the magnetic field of the wave? Give your answer in terms of μ and Bo. ▸ View Available Hint(s) (up) = Submit Part E IVE ΑΣΦ From the previous results, derive an expression for (u), the average energy density in the whole wave. Express the average energy density in terms of En and Eg only. The Poynting vector 5 gives the energy flux per unit area of electromagnetic waves. It is defined by the relation S- EXB Ho Calculate the time-averaged Poynting vector (S) of the wave considered in this problem. Give your answer in terms of Eg, c and ep and unit vectors i, j, and/or k. Do not use μ or Bg.