Saturday, January 16, 2010

Maxwell's Equations in Phasor Form

In case the field quantities are sinusoidally time varying; the electric field E can be expressed as

E(x, y, z, t) = Ex (x, y, z, t)ax +Ey (x, y , z, t) ay + Ez (x, y, z, t) az

Where Ex = Exm cos(ωt+θx), Ey = Eym cos(ωt+θy), Ez = Ezm cos (ωt+θz). Here the magnitudes Exm, Eym, Ezm, and the phase angles θx, θy, θz, are independent of time but may depend on spatial coordinates, e. g., Exm (x, y, z), θx(x, y, z). Now Ex can be expressed as

That is, the first derivative of a sinusoidal varying field is jω times the field. Therefore, the Maxwell’s equations in phasor form can be expressed as: