Final ExamPHY2061 12-10-04 Name:_______________________ ___ Final Exam 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. 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: 2244 3.14159273Sr V rπππ=== e=×−16022 1019. C xx yy zzab ab ab⋅= + +ab()()()yz yz xz xz xy xyab ba ab ba ab ba×= − − − + −ab xyz 92201910 N m/C4Kπε==×12 2 208.8542 10 C / N mε−=× 604 1.257 10 T m /Akµπ−== × ⋅70210 T m / A4Kkcµπ−== = ⋅ c=×30 108. m/s 12122ˆqqKr=Fr 0q=FE enc0ESqdεΦ= ⋅ =∫ΕΑv 0BSdΦ= ⋅ =∫B Αv 0ρε∇⋅=E 0∇⋅ =BBdNdtεΦ=− CSddddt⋅=− ⋅∫∫Es BAv t∂∇= −∂B×E0enc 0 0 0 0 0ECSS∫dddi d ddt dtµµε µ µεΦ⋅= + = ⋅ + ⋅∫∫BsjAEvA 00 0tµεµ∂+∂E×B∇=j V=−∇E 0UVq= CWU d=−∆ = ⋅∫Fs CVd∆=− ⋅∫Es ˆˆˆxyzxyz∂∂∇= + +∂∂∂∂ ()yxzFFFdivxyz∂∂∂∇⋅ = = + +∂∂∂FF VSdV d∇⋅ = ⋅∫∫FFΑv ()SCdd∇⋅= ⋅∫∫×F A F sv QCV=∆ ()22122QUCVC=∆= eff 1 2CCC=+ eff 1 2111CCC=+ ViR∆= 22 VPVi iRR== = eff 1 2RRR=+ eff 1 2111RRR=+ LRAρ= dqidt= FEvB=+×q() i=FL×B 3 iddkr=s×rB i=µA =τ r×F=τ µ×B U=−⋅µB zzzdBFdzµ= LdiVLdt∆= BNLiΦ= 212UL= i 220022EUBuVεµ== + RCRCτ= LRLRτ= 1LCLCω= SSPPNVVN∆=∆ Page 1 of 12Page 2 of 12 PHY2061 12-10-04 Name:_______________________ ___ c =×30 108. m J/s 1 eV =×−16022 1019. γ=−1122vc/ tt=γ 0 LL=0γ ()()2/xxvtttvxcγγ′=±′=± ′=′=yyzz21xxxuvuvuc±′=± 21yyxuuvucγ′=⎛⎞±⎜⎟⎝⎠ Emc=γ2()21Kmγ=− c pu=γm Fp= dd/ t2mc E pc24 2 22=− 112sin sinnnθθ= 01µ=×SEB avPISA== 2fωπ= 2kπλ= fvλ= ncvn= sindλθ=PHY2061 12-10-04 Name:_______________________ ___ 1. The electric field component of a traveling electromagnetic wave is described by (0ˆsinEkx)tω=Ez −, where E0 is a positive constant. (a) [6 points] What is the magnetic field component, both magnitude and direction? (b) [6 points] What is the average intensity of the wave per unit area perpendicular to the direction of the travel? (c) [6 points] What is the wavelength of the traveling wave if the angular frequency ? 1410 Hzω= Page 3 of 12PHY2061 12-10-04 Name:_______________________ ___ 2. [8 points] A light wave traveling horizontally strikes a glass prism with an index of refraction of n=1.5 as shown. The prism has a triangular cross section, with each interior angle measuring 60°. Calculate the angle relative to horizontal by which the light wave deflects after traversing both faces of the prism. 60° Page 4 of 12PHY2061 12-10-04 Name:_______________________ ___ 3. (a) [6 points] How much work is needed to accelerate a proton from a speed of 98.5% of the speed of light to 98.6% of the speed of light? The proton mass is , and its charge is . 271.67 10 kg−×191.6 10 Cqe−=+ = × (b) [6 points] If the proton travels enters a region where there is a constant magnetic field of 0.5 T perpendicular to direction of motion at its final velocity of 0.986c, what is the magnitude of the centripetal acceleration? Page 5 of 12PHY2061 12-10-04 Name:_______________________ ___ 4. [6 points] The electric field just outside of a spherical electric conductor of radius 3 cm is . What is the net electric charge contained in the conductor? 4ˆ , where 5 10 N/CCC==×Er Page 6 of 12PHY2061 12-10-04 Name:_______________________ ___ 5. The electric field in a certain region of space is given by 22ˆˆxyyx=+Exy. (a) [6 points] What is electric charge density in this region? (b) [6 points] What is the electric potential difference between 2 points on the x axis: x = 0 and x = a ? Page 7 of 12PHY2061 12-10-04 Name:_______________________ ___ 6. [6 points] Aluminum has a resistivity of 82.75 10 m−×Ω⋅ . A length of wire is made by extruding 7 m of aluminum through a hole of diameter 4 mm. What will be the resistance of the wire? 7. [8 points] A flat nonconducting surface infinite in extent carries a uniform charge density of . A small circular hole of radius has been cut in the middle of the sheet as shown. Calculate the electric field at a point z = 5 m away from the center of the hole along an axis perpendicular to the surface. (In other words, consider , but don’t set exactly equal to zero. You may find the superposition principle handy.) 9710 C/mσ−=×21.5 mR =zR /zR Z R (Space provided on next page) Page 8 of 12PHY2061 12-10-04 Name:_______________________ ___ 7. continuedPage 9 of 12PHY2061 12-10-04 Name:_______________________ ___ 8. [6 points] Two infinitely long straight wires have a circular cross section and are parallel to each other. One has a radius of 3mm and the other has a radius of 2mm. They are covered with an insulating material of negligible thickness. The two wires are parallel to each other, but carry a current of 5A in opposite directions. If the central axes of each wire are separated by 5mm, calculate the magnitude of the magnetic field at a point 5mm to right of the center of the 2mm radius wire along the line joining the two axes, as shown: 5mm 5mm 2mm radius, current out 3mm radius, current in Find field here :⊗Page 10 of 12PHY2061 12-10-04 Name:_______________________ ___ 9. A square loop of wire with a side length of 50 cm is rotated about an axis that bisects the square and that is perpendicular to a constant magnetic field of 0.5 T as shown (the square loop extends into the plane of the paper). The rotational frequency is 60 revolutions per second. (a) [6 points] Calculate the induced EMF in the loop of wire. (b) [6 points] If the wire has a resistance of 0.5 Ω, calculate the average power dissipated in the circuit. i⊗ωB axis :Page 11 of 12PHY2061 12-10-04 Name:_______________________ ___ 10. Consider the circuit below. Each capacitor has a capacitance of 2 µF, and each resistor has a resistance of 300 Ω. +ε (a) [6 points] Calculate the RC time constant of the circuit. (b) [6 points] Once a 6 V battery is connected, how much time must elapse before the
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