Halliday, Resnick & Walker — Interference: Problem 64

64. In the double-slit experiment of Fig. 35-10, the electric fields of the waves arriving at point P are given by \[ E_1 = (3.50 \, \mu\text{V/m}) \sin[(1.26 \times 10^{15})t] \] \[ E_2 = (3.50 \, \mu\text{V/m}) \sin[(1.26 \times 10^{15})t + 21.5 \, \text{rad}] \], where time \( t \) is in seconds. (a) What is the amplitude of the resultant electric field at point P? (b) What is the ratio of the intensity \( I_P \) at point P to the intensity \( I_{\text{cen}} \) at the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. In a phasor diagram of the electric fields, (d) at what rate would the phasors rotate around the origin and (e) what is the angle between the phasors?