An electromagnetic wave propagating in a vacuum is described by the magnetic field equation B = B₀ (kx - t) . Which of the following expressions represents the total average energy density of this wave?

Step-by-step solution

The instantaneous energy density of the magnetic field is u_B = B^2 2 ₀ = B₀^2 ^2(kx - t) 2 ₀ . The average value of ^2(kx - t) over a complete cycle is 1 2 . Thus, the average magnetic energy density is u_B = B₀^2 4 ₀ . In an electromagnetic wave, the energy is equally shared between the electric and magnetic fields. Therefore, the total average energy density is twice the average magnetic energy density: u = 2 u_B = 2 ( B₀^2 4 ₀ ) = B₀^2 2 ₀ . Answer: B₀^2 2 ₀