Page 1 of 13 PHY2061 11-9-06 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 at least 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 = 61 C 10 Cμ−= 61F 10 Fμ−= 121 pF 10 F−= 191 eV 1.6 10 J−=× 92201910 N m/C4Kπε==× 12 2 208.8542 10 C / N mε−=× c =×30 108. m/s 70210 T m / A4Kkcμπ−== = ⋅ 604 1.257 10 T m /Akμπ−== × ⋅ 0021cμε= 12122ˆqqKr=Fr 0q=FE enc0ESqdεΦ= ⋅ =∫ΕΑv 0ρε∇⋅=E V=−∇E 0UVq= CWU d=−Δ = ⋅∫Fs CVdΔ=− ⋅∫Es qVCΔ= diVLdtΔ=− dqidt= eff 1 2CCC=+ eff 1 2111CCC=+ LRAρ= RCRCτ= LRLRτ= eff 1 2RRR=+ eff 1 2111RRR=+ ViRΔ= 22 VPVi iRR== = 22QUC= 212ULi= 12 fLCωπ== γ=−1122vc/ tt=γ 0 LL=0γ ()()2/xxvtttvxcγγ′=±′=± ′=′=yyzz 21xxxuvuvuc±′=± 21yyxuuvucγ′=⎛⎞±⎜⎟⎝⎠ Emc=γ2 ()21KEmcγ=− FEvB=+×q() i=FL×B pu=γm Fp=ddt/ mc E pc24 2 22=− 03 4iddrμπ=s×rB 0encCdiμ⋅=∫Bsv 0wire2iBrμπ= 04arciBRμπ=Φ pqBr= =τ r×F Ni=μA =τμ×B U=−⋅μB zzzdBFdzμ= BSdΦ= ⋅∫B Α BdNdtεΦ=− BLNiΦ= 220022EBuεμ=+ xxyyzzab ab ab⋅= + +ab ()()()yz yz xz xz xy x yab ba ab ba ab ba×= − − − + −ab xyzPage 2 of 13 PHY2061 11-9-06 Name:_______________________ ___ 1. [8 points] In the circuit shown, the resistance112R=Ω . The battery voltages are identical:123 1 Vεεε=== . What is the current (in amps) flowing through the middle branch from a to b? 1Page 3 of 13 PHY2061 11-9-06 Name:_______________________ ___ 2. [6 points] A capacitor of capacitance 10210 FC−=× contains a charge q on one of its plates (and –q on the other). It is connected in to a resistor of resistance R = 200Ω such that it forms a closed circuit. How much time must elapse so that the charge on the capacitor is reduced to only 10% of its starting value? 3. [6 points] A stationary flat conductor carries a constant current i >0 in the direction from top to bottom (ˆ−y) in the presence of a magnetic field B that points into plane the paper (ˆ−z). If the electrons that make up the current are not allowed to leave the conductor, and the magnitude of their drift velocity is dv , indicate the direction and determine the magnitude of any electric field created inside the conductor. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x i B x y zPage 4 of 13 PHY2061 11-9-06 Name:_______________________ ___ 4. [6 points] An electron is accelerated from rest between 2 electric plates with a potential difference of 5510 VVΔ=× . What is the velocity of the electron upon reaching the far plate? (Careful!) The mass of the electron is 319.11 10 kgem−=×.Page 5 of 13 PHY2061 11-9-06 Name:_______________________ ___ 5. [6 points] A long wire has an electric charge density of 2.5 / mCλμ=+ , where 6110CCμ−= , as measured in the rest frame of the wire. What is the magnitude of the electric field in the rest frame of an electron traveling at a velocity of 82.8 10 m/sv =× parallel to the wire at a distance 1 cmr = from the wire?Page 6 of 13 PHY2061 11-9-06 Name:_______________________ ___ 6. [6 points] A long cylindrical wire of radius r = 3mm carries 100A of current. If the current density is uniform throughout the cross-section of the wire, what is the magnitude of the magnetic field at a radius of r = 1mm within the wire?Page 7 of 13 PHY2061 11-9-06 Name:_______________________ ___ 7. [8 points] An infinitely long insulated wire carrying a current I = 50 A is bent into a 270º arc (3/2πradians) of radius R=2 cm. The current comes in from infinitely far away from above, and exits to the left infinitely far away. Find the magnitude of the field B at the center of the arc. The wire begins and ends its turn at the locations indicated. R IR IIx y zPage 8 of 13 PHY2061 11-9-06 Name:_______________________ ___ 8. A stationary neutral atom resides at the center of a Cartesian coordinate system and has a magnetic dipole moment of 232.1 10 J/T−× aligned in the ˆ+y direction. (a) [6 points] What is the ratio of the magnitude of the magnetic field from the atomic dipole at y = 100 nm to that at y = 25 nm? (The radius of the atom is about 0.1 nm, where 1 nm = 10-9 m) (b) [6 points] If a magnetic field is present everywhere with the form 00ˆ , where 0.5 T/mBBy B==y , what is the magnitude of the acceleration of the dipole if the mass of the atom is 10-25 kg.Page 9 of 13 PHY2061 11-9-06 Name:_______________________ ___ 9. [6 points] The magnetic field of a large solenoid is used to keep a proton in a perfect circular orbit. The solenoid has 1000 windings per meter of length and has a radius of 1 m. If the proton has a velocity of 61.5 10 m/sv =× , what is the minimum current needed to keep the proton orbiting within the confines of the solenoid in a plane perpendicular to the solenoid axis? The proton mass is 271.67 10 kgpm−=× and its charge is 191.6 10 Cq−=× . p rPage 10 of 13 PHY2061 11-9-06 Name:_______________________ ___ 10. [6 points] A rod of length L = 0.5 m and mass m = 0.5 kg carries a current I = 20 A in the direction shown. The rod is aligned parallel to the z axis, and a uniform magnetic field is present: 00ˆ, 0.5 TBB B=− =y . The rod is suspended by two massless wires which bring the current to and away from the rod. The acceleration due to gravity is 10 m/s2 in the ˆ−y direction. What is the angle θ that the suspension wires make with respect to the magnetic field direction? θ I B y x zPage 11 of 13 PHY2061 11-9-06 Name:_______________________ ___ 11. An oscillating LC circuit consists of a 0.002 H inductive coil and a 4 μF capacitor. The capacitor has a voltage drop of 0.75 V when the current through the coil is 0.03A. (a) [6 points] Find the maximum charge on the capacitor. (b) [6 points] Find the maximum current through the coil.Page 12 of 13 PHY2061 11-9-06 Name:_______________________ ___ 12. [6 points] A circular conducting loop of wire increases in radius with time according to
View Full Document