Problem Set 13


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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Turn in at your table during class labeled with your name and group (e.g. L01 8A) Problem Set 13 – Your FINAL Pset Due: Wednesday, December 5 th at class beginning (before 10:15/12:15) Problem 1: Solve the Energy Crisis Energy is probably the biggest issue facing the world right now (if you are looking for soething important to do, think about this – the very existence of human life may hinge on our solving this problem). In a nutshell, we currently use fossil fuel to generate energy. This creates greenhouse gasses, which lead to global warming. a) What is the average power the average American uses (averaged over the year)? Include all energy use, not just electricity. What does that work out to for all of America? b) Let’s say that we want to get that all from nuclear power. Assuming that an average nuclear power plant generates 1 GW of power, how many do we need to power the US? c) If we were to get it from solar energy, how large an area would we need to cover with solar cells? The solar power at the earth is about 1.4 kW/m 2 . d) What happens to these numbers if we also want power for China and India to use energy at the same per capita rate? e) What will we need 30 years from now assuming current population growth rates? Analytic Problem… Problem 2: Coaxial Cable and Power Flow A coaxial cable consists of two concentric long hollow cylinders of zero resistance; the inner has radius , the outer has radius , and the length of both is , with a b l l >> b , as shown in the figure. The cable transmits DC power from a battery to a load. The battery provides an electromotive force ε between the two conductors at one end of the cable, and the load is a resistance R connected between the two conductors at the other end of the cable. A current I flows down the inner conductor and back up the outer one. The battery charges the inner conductor to a charge and the outer conductor to a charge . Q Q + (a) Find the direction and magnitude of the electric field E G everywhere. (b) Find the direction and magnitude of the magnetic field B G everywhere. (c) Calculate the Poynting vector in the cable. G S G (d) By integrating S over appropriate surface, find the power that flows into the coaxial cable. (e) How does your result in (d) compare to the power dissipated in the resistor? PS13 - 1
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PS13 - 2 AMPLE EXAM (25 pts) S he following exam is similar to what you should expect to find on Thursday evening, December he exam is out of 100 points. It consists of the following: ts total) each, 75 pts total) s a homework problem this exam is worth 25 pts. It will be graded like homework problems, T 6 th (7:30 – 9 pm in Walker). Please note that the exam is closed notes and that calculators are not allowed. I strongly recommend that you take this sample exam under the same conditions.
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