Exam 2PHY2061 11-8-05 Name:_______________________ ___ Exam 2 Closed book exam. A calculator is allowed, as is one 8.5×11” sheet of paper with your own written notes. Please show all work leading to your answer to receive full credit. Numerical answers should be calculated to 2 significant digits. Exam is worth 100 points, 25% of your total grade. UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this exam.” Sphere: 2344 3.14159273Sr V rπππ=== e=×−16022 1019. C 29.8 m/sg = 1 C 610 Cµ−=61F 10 Fµ−=121 pF 10 F−=191 eV 1.6 10 J−=×9201910 N m/C4Kπε==×2. m /s 12 2 208.8542 10 C / N mε−=×c =×30 10870210 T m / A4Kkcµπ−== = ⋅ 604 1.257 10 T m /Akµπ−== × ⋅0021cµε= 12122ˆqqKr=Fr 0q=FE enc0ESqdεΦ= ⋅ =∫ΕΑv 0ρε∇⋅=E V=−∇E 0UVq= CWU d=−∆ = ⋅∫Fs CVd∆=− ⋅∫Es QCV=∆ ()22122QUCVC=∆= eff 1 2CCC=+ eff 1 2111CCC=+ LRAρ= dqidt= RCRCτ= eff 1 2RRR=+ eff 1 2111RRR=+ ViR∆= 22 VPVi iRR== = γ=−1122vc/ tt=γ 0 LL=0γ ()()2/xxvtttvxcγγ′=±′=± ′=′=yyzz21xxxuvuvuc±′=± 21yyxuuvucγ′=⎛⎞±⎜⎟⎝⎠ Emc=γ2()21KEmcγ=− pu=γm Fp= dd/ t mc E pc24 2 22=− FEvB=+×q() i=FL×B3 iddkr=s×rB 0encCdiµ⋅=∫Bsv0wire2ˆˆ2ikirrµπ==Brr i=µA =τ r×F=τ µ×B U=−⋅µB zzzdBFdzµ= BSdΦ= ⋅∫B Α BdNdtεΦ=− xx yy zzab ab ab⋅= + +ab ()()()yz yz xz xz xy x yab ba ab ba ab ba×= − − − + −ab xyz Page 1 of 12PHY2061 11-8-05 Name:_______________________ ___ 1. An RC circuit is discharged by closing a switch at time t = 0. The initial potential difference across the capacitor is 5 V. The potential difference across the capacitor drops to half of its value in 35 ms. (a) [6 points] What is the time constant of the circuit? (b) [4 points] If the total resistance in the circuit is 10 kΩ, what is the capacitance? Page 2 of 12PHY2061 11-8-05 Name:_______________________ ___ 2. [8 points] In the circuit shown, the resistances are16R=Ω , 212R=Ω , and . The battery voltages are 324R =Ω118 Vε= and 26 Vε=. What is the current (in amps) flowing through the battery with potential difference1ε? Page 3 of 12PHY2061 11-8-05 Name:_______________________ ___ 3. [6 points] Two identical amounts (volumes) of copper are formed into two cylindrical rods, the first of length L and the second of length L/2. If the resistances of the two volumes (measured between the two ends) are 1R and 2R respectively, what is 2/1RR ? 4. [6 points] A large flat non-conducting sheet has an electric charge density of , where , as measured in the rest frame of the sheet. What is the charge density “seen” by an electron traveling at a velocity of parallel to the surface of the sheet? 25.0 / mCσµ=6110Cµ−= C82.9 10 m/sv =× Page 4 of 12PHY2061 11-8-05 Name:_______________________ ___ 5. [6 points] Galaxy A is reported to be receding from us at a speed of 0.41c. Galaxy B, located in precisely the opposite direction, is found to be receding from us at the same speed. What recessional speed would an observer on Galaxy A find for Galaxy B? 6. [6 points] An electron is accelerated from rest by a potential difference of 10,000 V. It then enters a uniform magnetic field of magnitude 0.05 T with its velocity perpendicular to the direction of the field. Calculate the radius in meters of its path in the magnetic field. The mass of the electron is . 319.11 10 kg−× Page 5 of 12PHY2061 11-8-05 Name:_______________________ ___ 7. The rectangular-shaped loop shown in the figure is carrying a current i = 2A in the clockwise direction shown. The length of the vertical sides is 7cm and the length of the horizontal sides is 3.5 cm. A uniform magnitude field B = 0.05T makes an angle θ=30° with respect to the plane of the loop. (a) [6 points] What is the magnitude of the torque acting on the loop if the left side is connected to a hinge? (b) [6 points] If the loop is free to rotate about its hinge due to the torque, by how much will the potential energy of the loop change when the torque becomes zero? Page 6 of 12PHY2061 11-8-05 Name:_______________________ ___ 8. [8 points] A long straight wire carries a current 180Ai= in the horizontal direction shown. Below it is a square loop of side length 50 cmb= carrying a current in the clockwise direction shown. The distance between the top of loop to the long straight wire is distance a, which you can take to be much smaller than b ( ). If the mass of the loop is 10 g, what is the maximum distance a such that the loop is attracted to the wire with current with a force that overcomes the force of gravity? (the acceleration due to gravity points in the direction). 240Ai =abm =1iˆ−y bb Page 7 of 12PHY2061 11-8-05 Name:_______________________ ___ 9. [6 points] A horizontal power line carries a current of 3000A from south to north. Earth's magnetic field, with a magnitude of 60µT, is directed toward the north with a dip angle 60° downward into the Earth relative to the horizontal. Find the magnitude and direction (use compass directions) of the magnetic force acting on a 100 m length of power line. Page 8 of 12PHY2061 11-8-05 Name:_______________________ ___ 10. [8 points] An infinitely long insulated wire carrying a current I = 100 A is bent into the shape shown (straight line plus circle of radius R=3 cm with the currents in the direction shown). Find the magnitude of the field B at the center of the circle. Page 9 of 12PHY2061 11-8-05 Name:_______________________ ___ 11. [6 points] A conductor has a cylindrical cross section with a radius a = 2 mm. Inside, a cylindrical cut-out hole (non-conducting) is made as shown, where the radius of the cut-out is b = 0.5 mm and the distance between the center of the main conductor and the center of the cut-out is d = 1 mm. The magnitude of the current density in the conductor is. What is the magnitude of the magnetic field at a radius of mm from the center of the conductor along a line connecting to the center of the cut-out? [Hint: try using the superposition principle.] 510 A/mj =20.5r = Page 10 of 12PHY2061 11-8-05 Name:_______________________ ___ 12. A rectangular loop of wire of sides 2LL× is moving with constant speed v into a region
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