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**+ E

_{y}_{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

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:

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