Phasor Notation for an Eddy Current Solution

Time varying quantities that have the form

can be represented as rotating phasors in the complex plane. Using Euler's formula,

if a = wt + q, F(t) equals the real portion of e^j(wt+q):

Each time-varying quantity has the form F_me^jqe^jwt. The component F_me^jq is a complex constant that can be represented by a stationary phasor in the complex plane. The e^jwt component is a complex number that depends on t and can be represented as a rotating phasor in the complex plane. The phasor's projection on the real axis oscillates sinusoidally. It reaches a peak when parallel with the real axis, and crosses zero when parallel with the imaginary axis. Therefore, a phasor with q = 90^° represents a quantity that peaks 90 degrees after a phasor with q = 0^°.