Mumbai University > Electronics Engineering > Sem 5 > Electromagnetic Engineering

Marks: 5 Marks

Year: Dec 2014

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

$∇^2=\dfrac{d}{dx^2}+\dfrac{d}{dy^2}+\dfrac{d}{dz^2} \ \ \ \ \ (∇^2 \text{is scalar operator})$

The wave equation for each scalar component is –

$∇^2 ψ= -w^2 μ ϵ ψ$

Where,

$ψ \text{Could be} E_x,E_y,E_z or H_x,H_y,H_z$