Problem Set 4


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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Problem Set 4 Due: Wednesday, March 5 at 11 am. Hand in your problem set in your section slot in the boxes outside the door of 32-082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3 Group A) Problem 1 (10 points): What, approximately, is the capacitance of a typical MIT student? Check out the exhibit in Strobe Alley (4 th floor of building 4) for a hint or just to check your answer. Hint: If you model the human being as a geometric object, what geometric object can you easily compute capacitance? Problem 2 ( 10 points) The English Channel tunnel consists of a series of tunnels, each with a set of railroad tracks. As an order of magnitude estimate, calculate the capacitance of an idealized tunnel, cylindrical in shape with a monorail which is also cylindrical and is coaxial to the tunnel. Both the outer and inner cylinders are conducting. The length of tunnel is l = 5 . 0 × 10 1 km , the diameter of monorail is d = 5 . 0 × 10 1 cm , and the diameter of tunnel is a = 1 . 0 × 10 1 m . a) Find the capacitance of this idealized tunnel. b) Does the capacitance increase, decrease, or stay the same when a train enters the tunnel? {Briefly} explain your reasoning. Problem 3: Capacitors (10 points) In the circuit shown at right C 1 = 2.0 μ F, C 2 = 6.0 μ F, C 3 = 3.0 μ F and 10.0V V Δ= . Initially all capacitors are uncharged and the switches are open. At time t = 0 switch S 2 is closed. At time t = T switch S 2 is then opened, proceeded nearly immediately by the closing of S 1 . Finally at t = 2 T switch S 1 is opened, proceeded nearly immediately by the closing of S 2 . Calculate the following: (a) the charge on C 2 for 0 < t < T (after S 2 is closed) (b) the charge on C 1 for T < t < 2 T (c) the final charge on each capacitor (for t > 2 T ) Problem 4: SAMPLE EXAM (20 points) The following exam is similar to what you should expect to find on Thursday evening, March 6 th (7:30 – 9:30 pm). 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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Physics 8.02 Exam One: PS 4 Spring 2008 23 ˆ 44 oo qq rr πε == Err G G ˆ points source q observer r r r= from to G inside o closed surface Q κ ε ⋅= ∫∫ EdA G G w points from inside to outside dA G q = FE GG = = Δ b a a b b to a from moving V V V s d E G G 0 = path closed s d E G G WU q V =Δ = Δ point charge 4 o q V r = = pairs all j i o j i q q U r r G G 4 2 1 2 ov o l UE d V ⎡⎤ = ⎢⎥ ⎣⎦ ∫∫∫ x E x = - V x , E y = - V y , E z = - V z r V E r =− for spherical symmetry Q C V = Δ U = 1 2 C Δ V 2 = Q 2 2C 12 parallel
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This note was uploaded on 11/10/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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