Midterm 2 Answers for B and D

Midterm 2 Answers for B and D - Physics 6B 1 February...

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Unformatted text preview: Physics 6B 1 +\ February 23,2011 KatsushiArisaka SO UL ‘ W Second Midterm (Type B pg 3 - Last Name: ARISA' kfl First Name: QTJIAJM Student ID No. Enrolled Lecture: 2 (Noon) / 3 (19m) Exam Time: Noon / 19m Important Remarks: 0 Sorry to tell you but during the exam, close books, close notes, no calculator is allowed; please just rely on your own brain. ' Please use any open space on the exam for your solution. Please write down how you derived concisely (which helps you to get a partial credit even if the final answer is wrong.) ° If you finish early, please be seated quietly until the exam time is over. ' Total is 100 points. Your Points: m—m _-_— "—— —-—— -_-_ _-_— “—— _— ——— A solid conducting sphere of radius R has a total positive charge +3Q. A conducting spherical shell of inner radius 3R and outer radius 4R is concentric with the solid sphere and has a total negative charge -3Q. Let r be the distance from the center of the sphere. First, please calculate the electric fields from inside out by applying Gauss’s law. a) Find the electric Field E inside the sphere (r < R). b) Find the electric Field E in the region between the sphere and the shell (as a function of r, for R < r < 3R). c) Find the electtie Field E inside the shell (3R < r < 4R). (1) Find the electric Field E outside the shell (as a function of r, for 4R < r). e) Plot the graph of F] below as a function of r. (Assume that the outward field has positive sign, and the inward field has negative sign.) 2 Next, let’s figure out the charge distribution in the previous questions a) Find the amount of the charge on the following surfaces: i) Outer surface of the share (r =R) ii) Inner surface of the shell (r :3R) fl iii) Outer surface of the shell (r :41?) D b) Plot the graph of the charge distribution as a function of r. 6) Draw the electric field lines on the picture below. 3 Next, let’s figure out the potential and the capacitance in the previous question. Please assume that V=0at r—->oo. a) Find the potential Voutside of the shell (4R < r). b) Find the potential Vinside the shell (3R < r < 4R). 6) Find the potential Vin the region between the sphere and the shell (R < r < 3R). d) Find the potential V inside the sphere (r < R). e) Plot the graph of the potential Vas a function of r. 4 This system consists of a pair of conductors. Therefore, it can be considered as a capacitor. a) Calculate the capacitance C. gage 3‘8 C? J I N H , IO 2%(é’3 ale b) Calculate the total potential energy stored in this capacitance (when it is charged up by +3Q and -3Q). U" —~LCV2=“L-gi-- (919.8) 5 As shown in the circuit below, five resistors, R1 = R2 = R3 = R4 = R5 = 3 Q, are connected to a battery, 8 = 36 V. Assume that the potential at the point A is 0 V. Calculate the following quantities. litJ = 3 n B E a) Equivalent resistance Reg. b) Total current I (which goes through the battery.) c) Total amount of power P dissipated in this entire circuit. R‘=3fl mow D F 6 As shown in the circuit below, five resistors, R1 = R2 = R3 = R4 = R5 = 3 Q, are connected to a battery, 8 = 36V. Assume that the potential at the point A is 0 V. This time, a conducting wire directly connects points B and F. Calculate the following quantities. Rs 3 3 D B E 3.) Equivalent resistance Reg. b) Potential VF at the point F. c) Current 15 which goes through the resistor R5. d) Potential V5 at the point E. e) Current 13 which goes through the resistor R3. R.=3fl man a F 7 As shown in the circuit below, five resistors, R1 = R2 = R3 = R4 = R5 = 352, are connected to a battery, 8 = 36V. Assume that the potential at the point A is 0 V. This time, conducting wires directly connect points C and E, as well as C and F . Calculate the following quantities. B 55:30 5.) Equivalent resistance Reg. b) Potential V5 at the point E. c) Current 13 which goes through the resistor R3. (1) Potential VF at the point F. e) Current 14 which goes through the resistor R4. my) B 52-39 F 09 ,_ I: 3 3s a , RefM‘flfE .0. 3 fig} ‘ LS ...
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