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Derive wave equations for time harmonic fields.

Mumbai University > Electronics Engineering > Sem 5 > Electromagnetic Engineering

Marks: 5 Marks

Year: Dec 2014

1 Answer
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Consider time harmonic fields with angular frequency

$F (x,y,z,t)= F(x,y,z).e^{jwt}$

The derivatives with respect to time are:

$\dfrac{d}{dt}=jw \\ \dfrac{d^2}{dt^2}=jw.jw= -w^2$

The wave equation is-

$∇^2 E= -w^2 μ ϵ E \\ ∇^2 H= -w^2 μ ϵ H$

Each component of E and H satisfies the wave equation

$∇^2=\dfrac{d}{dx^2}+\dfrac{d}{dy^2}+\dfrac{d}{dz^2} \ …

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