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Homework set 2, due Monday September 14, 2015, 10:30 am 1. (20 points) Imagine an electromagnetic plane wave in vacuum whose E-field (in SI units) is given by Determine the speed, frequency, wavelength, period, initial phase, E-field amplitude and polarization. Write an expression for the magnetic field associated with the wave. 2. (20 points) A plane electromagnetic harmonic wave of frequency 600 x 1012 Hz (green light), propagating in the positive x-direction in vacuum, has an electric field amplitude of 42.42 V/ m. The wave is linearly polarized such that the plane of vibration of the electric field is at 45 ° to the xz-plane. Write expressions for E and B. 3. (20 points) A focused C02 laser beam putting out a continuous wave (=10,600 nm) of 3 kW is capable of burning a hole through a quarter-inch thick stainless steel slab in about 10 seconds. Determine the irradiance when such a beam has a focused spot area of 10 − 5 cm2. What is the electric field amplitude? 4. (20 points) Tiny glass spheres have been suspended in midair on a beam of laser light. What is the force on a perfectly reflecting 9 × 10 −2-cm 2 surface arising from a 600-W collimated laser beam having a cross-sectional area of 4 mm2? 5. (20 points) Consider a linearly polarized plane electromagnetic wave traveling in the +x-direction in free space having as its plane of vibration the xy plane. Given that its frequency is 10 MHz and its amplitude is E0= 0.08 V/m (a) Find the period and wavelength of the wave. (b) Write an expression for E(t) and B(t) (c) Find the flux density, <S>, of the wave.