PHYS-115(x) (Kaldon-xxxxx) Name ______________________________________________WMU - Winter 2001Exam 2 - 100,000 points Book Title __________________________________________Section: 3a 3b 3c 3d Sample Exam A to F G to M N to S T to Z 01/23/2001•Rev.5State Any Assumptions You Need To Make -- Show All Work -- Circle Any Final AnswersUse Your Time Wisely - Work on What You Can - Be Sure to Write Down EquationsBOLDFACE Variables Are Vectors - Feel Free to Ask Any Questions“There I Was, Officer, Minding My Own Business, When All Of A Sudden…” (50,000 pts.)1.) A proton ( q = +e , mp = 1.67×10-27 kg ) is moving along withvelocity rvmsi=´138 106./$, when a magnetic field, B, is suddenlyturned on in the +z-direction as shown. The radius of the circular orbit is2.00 meters. (a) What is the magnitude of the magnetic field B ? (b) If an electric field vector, rE , is turned on after one circle such that theproton’s velocity vector rvmsi=´138 106./$never turns, find the electric field vector, rE . (c) A 157 W resistor is made of three identical resistors ( R = R1 = R2 = R3 ) as shown. Find R.(d) A 157 mF capacitor is made of three identical capacitors ( C = C1 =C2 = C3 ) as shown. Find C.(e) At t = 3t, a series RC circuit’s current drops to about 5% of its initial value, I0 . If R = 157 W andC = 157 mF, what time is this?Physics 115 / Exam 1 Winter 2001 Page 2This Physics is Past Your Capacity to Resist (50,000 pts.)2.) (a) The following circuit can be reduced to a single equivalentcapacitor by network reduction. At each step in the reduction,circle the capacitors you are going to reduce, mark them asSERIES or PARALLEL, then draw the next equivalent circuitdown to (and including) the final circuit. DO NOT WRITEDOWN OR TRY TO SOLVE THE EQUATIONS THAT GOWITH EACH CIRCUIT.(b) The following circuit cannot be reduced by network reduction to a single equivalent capacitance. However,if C1 = C2 = C4 = C5 = 100. pF, you can easily find the charges ±Q3 on the plates of C3. Find Q3 and BRIEFLYexplain your reasoning. Hint: You might want to consider what is the voltage difference V3 across the capacitorC3.(c) The following diagram is correct “as Dr. Phil intended it”, even if it looks funny. All the resistors are 111 W.Find Req for this circuit.(d) An RC circuit has R = 105 kW and C = 151 mF. Find the time t when the fully charged capacitor willdischarge to 85.0%, q(t) = 0.850 Q0 .(e) A charge q = -1.03×10 -6 C is moving at vx = +3.37 m/s ; vy = vz = 0 when it experiences a magnetic fieldBx = 2.00 T ; By = 2.00 T ; Bz = 0. Find the magnetic force vector rFB acting on the charge q.Physics 115 / Exam 1 Winter 2001 Page 3No Moving Electric Charges in Miami After Hurricane Wilma… (50,000 points)3.) A parallel plate capacitor consists of two metal plates, each 5.00 cm wide by 10.0 cm long, with a gap d =2.00 mm. The space between the plates is filled with silicone oil (dielectric constant k = 2.50 and dielectricstrength 15.0 × 106 V/m). (a) Show whether you can safely charge this capacitor with DV = 25,000 volts.(b) Consider four identical 625 W resistors and a 16.55 volt battery. Find the maximum and the minimumequivalent resistance you can make with these resistors. Be sure to draw the two circuit diagrams for full credit.(c) A brand fresh 6.00 volt battery acts like a perfect battery at time t = 0 and delivers a current of 1.63 A. Atsome later time, as the real battery weakens, the current drops to 1.51 A. Find the power dissipated by theinternal resistance inside the real battery when I = 1.51 A.(d) A proton ( q = +e , mp = 1.67×10 -27 kg ) is moving along with velocityrvmsi= 138./$, when a magnetic field, B = 1.439 × 10 -4 T, is suddenlyturned on in the +z-direction as shown. Find the radius r of the circularpath the proton makes.(e) Pages 157-158 of Penn & Teller’s How to Play With Your Food talks about “The Incredibly DangerousGlowing Pickle Machine.” † Here an ordinary dill pickle is skewered at the ends with two metal prongs, whichare then hooked up to 110. volts of potential difference. If the current flowing through the green glowing pickleis 5.00 A, and the pickle is roughly 2.00 cm × 2.00 cm × 10.0 cm long, calculate the resistivity r of the pickle. † Does Dr. Phil really have to tell you DO NOT TRY THIS AT HOME? Okay, I will. DO NOT TRY THIS AT HOME!Physics 115 / Exam 1 Winter 2001 Page 4Don’t Panic. Just Follow the Wires and Make the Connections (50,000 points)4.) (a) You are given two square metal plates with sides a = 5.00 cm. Design an air filled capacitor, such thatwhen hooked up to a 9.00 volt battery and fully charged, it will spark across the gap and discharge. What is thecapacitance C of this badly designed capacitor? Do not say that the answer is zero… (grin).(b) A brand fresh 6.00 volt battery acts like a perfect battery at time t = 0 and delivers a current of 1.63 A. Atsome later time, as the real battery weakens, the current drops to 1.51 A. Find the internal resistance r of theweak battery. (c) A 311 W resistor is made of three identical resistors ( R = R1 = R2 = R3 ) as shown. Find R.(d) A 311 pF capacitor is made of three identical capacitors ( C = C1 = C2 = C3 ) as shown. Find C.(e) A particular circuit generates 125 W of Joule heating when hooked up to a perfect battery which has apotential difference of 6.00 volts. If the perfect battery is replaced with another perfect battery of half thevoltage, find the power dissipated by Joule heating in this new