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) = E_x (x, y, z, t)a_x +E_y (x, y , z, t) a_y + E_z (x, y, z, t) a_z

Where E_x = E_xm cos(ωt+θ_x), E_y = E_ym cos(ωt+θ_y), E_z = E_zm cos (ωt+θ_z). Here the magnitudes E_xm, E_ym, E_zm, and the phase angles θ_x, θ_y, θ_z, are independent of time but may depend on spatial coordinates, e. g., E_xm (x, y, z), θ_x(x, y, z). Now E_x can be expressed as

Maxwell's Equations

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:

Maxwell's Equations in Phasor Form