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HW3_solutions_EE325_Sp12

HW3_solutions_EE325_Sp12 - Solutions EE 325 Spring 2012 HW...

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Solutions: EE 325 Spring 2012, HW 3, self-graded copies due Wed. Feb. 15. 1 1. 1. Hayt 3.1 : An empty metal paint can is placed on a perfectly insulating table, the lid is removed, and both parts are discharged (honorably) by touching them to ground. An insulating nylon thread is glued to the center of the lid, and a penny, a nickel, and a dime are glued to the thread so that they are not touching each other. The penny is given a charge of +5nC, and the nickel and dime are discharged. The assembly is lowered into the can so that the coins hang clear of all walls, and the lid is secured. The outside of the can is again touched momentarily to ground. The device is carefully disassembled with insulating gloves and tools. a) What charges are found on each of four metallic pieces (three coins and a paint can/lid assembly)? b) If the penny had been given a charge of +5nC, the dime a charge of -2nC, and the nickel a charge of -1nC, what would the final charge arrangement have been? a) All coins were insulated during the entire procedure, so they will retain their original charges: Penny: +5nC; nickel:0; dime:0. Since the electric field must be zero outside of grounded metal can, the net flux of an electric field outside of the can is zero. This means that the charge enclosed is zero, which means that the walls of a can (with a lid) have an equal and opposite negative charge (-5nC) to the penny inside. Therefore, the can plus lid retained a net charge of -5nC after disassembly. Since we didn’t give you any details about the geometry of the can and lid you can’t tell how the charge split between the can and the lid. b) Again, since the coins are insulated, they retain their original charges. The charge induced on the walls of a grounded can (with a lid) is equal to negative the sum of the coin charges, or -2nC. This is the charge that the can/lid contraption retains after grounding and disassembly.
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Solutions: EE 325 Spring 2012, HW 3, self-graded copies due Wed. Feb. 15. 2 2. Hayt 3.5 : Let 2 2 4 4 4 ˆ ˆ 4 2 4 x y z Coul Coul Coul D xya x z a yza meter meter meter All the coordinates (x, y, and z) are measured in meters, and the unit vectors do not have dimensions, just direction. Constants have units as specified. a) What are the units of D ? Write out the dimensional analysis. b) Evaluate surface integrals to find the total charge enclosed in the rectangular parallelepiped 0< x <2m, 0< y <3m, 0< z <5m: Of the 6 surfaces to consider, only two will contribute to the net outward flux. Two will produce no flux and two other surfaces will produce the fluxes that will cancel one another (why?).
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