HW-230B-1_2010

HW-230B-1_2010 - ECE 230B, HW-1, Winter 2010 1. 3-D Gauss...

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ECE 230B, HW-1, Winter 2010 1. 3-D Gauss’ law is obtained after a volume integration of 3-D Poisson’s equation and takes the form of E = ∫∫ dS Q si S ε , where the LHS is an integral of the normal electric field over a closed surface S , and Q is the net charge enclosed within S . Use it to derive the electric field at a distance r from a point charge Q (Coulomb’s law). What is the electric potential in this case? 2. (a) Use Gauss’ law to show that the electric field at a point above a uniformly-charged sheet of charge density Q s per unit area is Q s /2 , where is the permittivity of the medium. (b) For two oppositely-charged parallel plates with surface charge densities Q s and - Q s , show that the electric field is uniform and equals Q s / in the region between the two plates, and is zero in the regions outside the two plates. 3. Assume silicon, room temperature, complete ionization. An abrupt p-n junction with N a = N d = 10 17 cm -3 is reversed biased at 2.0 V.
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