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6.24 The magnetic field in a dielectric material with μ = μo, and o=0 is given by H(y, t) = x5 cos(27 x 107t + ky) (A/m). Find k and the associated electric field E. 4€0,

6.24 The magnetic field in a dielectric material with μ = μo, and o=0 is given by H(y, t) = x5 cos(27 x 107t + ky) (A/m). Find k and the associated electric field E. 4€0,

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: 4€0, *6.24 The magnetic field in a dielectric material with € = μ = μo, and o = 0 is given by H(y, t) = x5 cos(2л × 10²t+ky) Find k and the associated electric field E. (A/m).
Transcribed Image Text:: 4€0, *6.24 The magnetic field in a dielectric material with € = μ = μo, and o = 0 is given by H(y, t) = x5 cos(2л × 10²t+ky) Find k and the associated electric field E. (A/m).
Expert Solution
Step 1

Maxwell equations for Electromagnetic waves:

The four Maxwell equations define the four basic laws of electromagnetism. The Four Maxwell equations are,

∇→·E→=ρε                                   . . . (1)∇→·H→=0                                     . . . (2)   ∇→×E→=-μ∂H→∂t                      . . . (3)    ∇→×H→=J→+∈∂E→∂t                   . . . (4)   

where ρ is the volume charge density and J→ is the current charge density. The current charge density is given by the equation,

J→=σE→                                       . . . (5)

 

An equation of the form

 H→ (y,t)=x^ Acos(ωt-ky) 

represents an electromagnetic wave propagating in the y direction with a magnetic field oscillating in the x direction. For these types of waves propagation constant k is given as,

k=ωv

where v=1μ∈.

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