20075ee1_1_HW3

20075ee1_1_HW3 - CHAPTER 3 3.1 An empty metal paint can is...

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CHAPTER 3 3.1. An empty metal paint can is placed on a marble 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 +5 nC, 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 the five metallic pieces? All coins were insulated during the entire procedure, so they will retain their original charges: Penny: +5 nC; nickel: 0 ; dime: 0 . The penny’s charge will have induced an equal and opposite negative charge (-5 nC) on the inside wall of the can and lid. This left a charge layer of +5 nC on the outside surface which was neutralized by the ground connection. Therefore, the can retained a net charge of 5nC after disassembly. 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? Again, since the coins are insulated, they retain their original charges. The charge induced on the inside wall of the can and 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. 3.2. A point charge of 20 nC is located at (4,-1,3), and a uniform line charge of -25 nC/m is lies along the intersection of the planes x = 4 and z = 6. a) Calculate D at (3,-1,0): The total ﬂux density at the desired point is D (3 , 1 , 0) = 20 × 10 9 4 π (1 + 9) a x 3 a z 1 + 9 point charge 25 × 10 9 2 π 49 + 36 7 a x 6 a z 49 + 36 line charge = 0 . 38 a x + 0 . 13 a z nC / m 2 b) How much electric ﬂux leaves the surface of a sphere of radius 5, centered at the origin?

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