(a) State Maxwell's equation for the curl of the magnetic and the electric field in free...

 

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(a) State Maxwell's equation for the curl of the magnetic and the electric field in free space. State the meaning of all the terms in the equations and identify the displacement current density. Using Maxwell's equations, derive the wave equations for B. Show that the wave equations admit plane waves for the electric and magnetic fields in free space of the form E = Ege(kz-wt), B = Boet(kz-wt) where Eo and Bo are constant vectors with real components if k? = w* Ho€o. Show that E and Bare transverse waves propagating with speed c = 3x 10° ms'. (b) Show that the wave number of an electromagnetic wave plane wave is complex in a material with conductivity o. Assume the wave is propagating along the y-axis. Determine the real and imaginary parts of the wave number in terms of w, u, ɛ and o. (a) State Maxwell's equation for the curl of the magnetic and the electric field in free space. State the meaning of all the terms in the equations and identify the displacement current density. Using Maxwell's equations, derive the wave equations for B. Show that the wave equations admit plane waves for the electric and magnetic fields in free space of the form E = Ege(kz-wt), B = Boet(kz-wt) where Eo and Bo are constant vectors with real components if k? = w* Ho€o. Show that E and Bare transverse waves propagating with speed c = 3x 10° ms'. (b) Show that the wave number of an electromagnetic wave plane wave is complex in a material with conductivity o. Assume the wave is propagating along the y-axis. Determine the real and imaginary parts of the wave number in terms of w, u, ɛ and o.