# ps3 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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------------------------------------------------------------------------------ MASSACHUSETTS INSTITUTE OF TECHNOLOGY± Department of Electrical Engineering and Computer Science± Problem Set No. 3 6.630 Electromagnetic Theory Issued: Fall Term 2006 Due: Reading assignment : Section 1.4-1.5, 1.9 ; J. A. Kong, “ Electromagnetic Wave Theory ,” EMW, 2005. Problem P3.1 The Earth receives over all frequency bands about 1 . 5kW / m 2 of power from the Sun. (a) The Earth-Sun distance is 150 × 10 9 m . How long does it take the sunlight to reach the Earth? (b) The Earth radius is 6400 km. What is the total power received by the Earth? (c) Assume the Sun’s mass is 2 × 10 30 kg which converts to radiated energy according to mc 2 at 1 percent eﬃciency. How long can the Sun radiate at the present level? (c) The Sun radiates 10 20 Wm 2 Hz 1 at 3GHz . Assuming constant power level over 1GHz bandwidth, what is the Poynting power density and the corresponding electric field amplitude? Problem P3.2 x y z B J - 0 Consider a slab of semiconductor with positive charge carriers of density N such that

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