102e198 - an. "Rica, law—a; ms FIRST HOURLY...

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Unformatted text preview: an. "Rica, law—a; ms FIRST HOURLY EXAM—— — PHYSICS 171.102 This exam is closed book and closed notes (but see the attached “formula sheet”). The maximum number of points for each problem is shown in parentheses. SHOW ALL WORK. Where part of a problem uses the result of an earlier part which you did not answer, the appropriate symbol may be substituted for that result. No partial credit will be given for an answer without supporting work being shown. No credit will be given when multiple answers are given to the same problem (even if one is correct). Answers should be written in pen (not pencil). Cross out mistakes (do not erase). The exam is from 8:00 to 8:50. Good luck! 1.(20 pts.) Consider the two charged particles shown below with charges as indicated. The charges are located along the x—axis. Q I as a. (10) Wherefon the x-aztis (other than at infinitedistance) is there a point at which the net electric field islzero: between the two charges, to their left, or to their right? Explain! X ~ QXIJ‘ b. (10) Are there points with zero net electric field anywhere 013" the x—axis (other than at infinite distance)? Explain your answer. Hint: 'sketch the electric field lines from each charge. 2. (25 pts.) A negative charge Q is placed at the center of an uncharged conducting spherical shell with an inner radius of a and and outer radius of b. a. (10) What effect does Q have on the distribution of charges in and on the conductor (a S r g b)? Specifically, what is total charge residing on the outer skin of the conductor (at r 2 b), on the inner skin (at r 2: a), and inside the conducting shell (a < r < b)? Explain. b. (5) Sketch the direction of the electric field in the three regions: r < or (inside the hollow cavity), a g r < b (in the shell), and r 2 b (outside). Explain. c. (10) Using Gauss’s Law, derive an algebraic expression for the magnitude of the electric field for each of the three regions in part b. 3. (25 pts.) Two capacitors, with capacitances CA and 03 respectively, are placed into a circuit as indicated below. The ideal battery in the circuit maintains a potential difference V0 2 9.0 Volts across its terminals. CA 2 2 CB, and both capacitors are fully charged. fi—fi 1*] WVO‘: “l \{olJrr CA T__m____:l—° a. (10) What is the resulting potential difference between the two plates of capacitor A? What about capacitor B? Explain. Cs b. (5) Sketch the direction of the electric field between the two plates of each capacitor. What is the numerical value for the magnitude of the electric field in capacitor A if the two plates . are separated by 0.01 meters? ' c. (10) The total amount of work done by the battery in fully charging the two capacitors was 0.81 Joules. What is the equivalent capacitance of the circuit (034, in Farads)? What are the values for CA and GB (in Farads)? 4. (30 pts.) Four identical resistors with R = 15 Q are placed into a circuit as indicated below, hooked up to an ideal battery that maintains a potential difference of 30 Volts. a. (10) Calculate the potential change across each resisitor ( in Volts), and indicate which side of the resistor is at the higher potential. ‘ b. (10) Calculate the Circuit’s equivalent resistance (Req) and total current (am, in Amperes). Hint: one of the resistors can be removed Without affecting R6,, or itot. c. (10) For each resistor, calculate the current ( in Amperes) and the rate of resistive dissipation (power loss to resistive heating, in Watts). ...
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102e198 - an. &amp;quot;Rica, law—a; ms FIRST HOURLY...

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