Question

# Two travelling sinosoidal electromagnetic waves, each with an intensity 15 W/m2W/m2 ﻿, interfere to form a...

Two travelling sinosoidal electromagnetic waves, each with an intensity 15 W/m2W/m2 ﻿, interfere to form a standing wave. The resulting electric field E⃗ (z,t)E→(z,t) has nodes (i.e., is zero at all times) at z=…,−2a,−a,0,a,2a,…z=…,−2a,−a,0,a,2a,… with aaa = 4.0 mm , and satisifes E⃗ (z,0)=0E→(z,0)=0. Furthermore, the magnetic field B⃗ (z,t)B→(z,t) is observed to point along ±i^±i^ everywhere. You may take ccc = 3.0×108 m/sm/s and 8.9×10−12 F/mF/m .

A) What is the wavelength λλlambda of the two constituent travelling waves?

B) When will the electric field be zero everywhere for the first time after t=0? Express your answer in units of ns.

c)When will the magnetic field be zero everywhere for the first time after t=0

d)What is the amplitude (maximum magnitude) of the electric field for the standing wave? Express your answer in units of V/m.

e)How far from the origin is the nearest point where the amplitude of the (instantaneous) Poynting vector is maximum? Express your answer in units of meters.

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