77777 77777Instructor(s): Reitze/KumarPHYSICS DEPARTMENTPHY2054 Final Exam December 11, 2010Name (print, last first): Signature:On my honor, I have neither given nor received unauthorized aid on this examination.YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.(1) Code your test number on your answer sheet (use lines 76–80 on the answer sheet for the 5-digit number).Code your name on your answer sheet. DARKEN CIRCLES COMPLETELY. Code your UFID number on youranswer sheet.(2) Print your name on this sheet and sign it also.(3) Do all scratch work anywhere on this exam that you like. Circle your answers on the test form. At the end of thetest, this exam printout is to be turned in. No credit will be given without both answer sheet and printout.(4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do notmake any stray marks or some answers may be counted as incorrect.(5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing. If youbelieve that no listed answer is correct, leave the form blank.(6) Hand in the answer sheet separately.Useful Constants:ke= 8.99 × 109Nm2/C2²0= 8.85 × 10−12C2/(Nm2) V=volt N=newtonµ0= 4π × 10−7Tm/A k0= µ0/(4π) = 10−7Tm/A c = 3 × 108m/s g = 9.8 m/s2electron charge = −1.6 × 10−19C electron mass = 9.11 × 10−31kg C=coulomb“milli”=10−3“micro”=10−6n=“nano”=10−9“pico”=10−12J=joule m=Meter1. Two equal and opposite point charges +Q and −Q are located on the y-axisat y = d/2 and y = −d/2 as shown in the figure. What is the magnitude ofthe electric field on the x-axis a distance x = d/2 from the origin?+Qd x -Q x-axisy-axis(1) 2.83keQ/d2(2) 1.41keQ/d2(3) 0.71keQ/d2(4) 5.6keQ/d2(5) 4keQ/d22. Four point charges form a square with sides of length L as shown in the figure.Three of the charges have charge +Q and one has charge −Q. What is theminimum amount of work that must be done (against the electric force), tomove the −Q charge to infinity?L+Q +Q +Q -Q L (1) 2.71keQ2/L (2) −0.91keQ2/L (3) −1.83keQ2/L (4) −1.41keQ2/L (5) 0.91keQ2/L3. Two equal and opposite point charges +Q and −Q each with a mass of 1 gramare released from rest 1 meter apart. They attract each other and fly towardeach other at speed V as shown in the figure. If Q = 1µC, what is their speed(in m/s) when they are 0.5 meters apart?vv(1) 3 (2) 1.5 (3) 6 (4) 9 (5) 2.14. A copper cable with resistivity ρ = 2.0 × 10−8Ω·m is designed to carry a current of 300 Amps with a power loss of 2Watts per meter of cable. What is the required radius of this cable (in cm)?(1) 1.69 (2) 1.41 (3) 0.83 (4) 2.35 (5) 0.6677777 777775. Two infinitely long parallel wires lie in the xz-plane and are located at x = −d/2and x = d/2 as shown. The left wire (x = −d/2) carries a current 2I (into thepage), while the right wire (x = d/2) carries a current I in the same direction(into the page). What is the y-component of the magnetic field on the x-axisat x = 0?I in x-axisy-axis2I in d(1) −µ0I/(πd) (2) −2µ0I/(πd) (3) 2µ0I/(πd) (4) µ0I/(πd) (5) −µ0I/(2πd)6. Three circular concentric loops of wire, each having 10 turns, are shown in thefigure. The inner loop has a radius of 10 cm, the middle loop has a radius of20 cm, and the outer loop has a radius of 35 cm. The current in the inner loopis I1= 2.0 A and the current in the middle loop is I2= 4 A. Both the innerand middle loop currents are traveling in a counterclockwise direction. Whatis the current I3(magnitude and direction) in the outer loop if the magneticfield at the center is 3.6 × 10−4T directed into the page?III = ?123(1) 34.0 A, clockwise(2) 8.5 A, clockwise(3) 14.0 A, counterclockwise(4) 8.5 A, counterclockwise(5) 32.0 A, clockwise7. In general the index of refraction of quartz depends on the wavelength of thelight. Suppose that a ray of light is incident normally on face ab of a quartzprism in the shape of an equilateral right triangle as shown with an index ofrefraction of the quartz that is inversely proportional to the wavelength, λ, ofthe light as given by the formula n = a/λ, with a = 735 nm. If the incidentlight has wavelength λ = 600 nm, what is the angle (in degrees) between thelight ray entering the quartz and the light ray that exits the quartz?b ac45o quartz 90oIncident LightAB air(1) 15 (2) 90 (3) 10 (4) 5 (5) 458. A conducting bar with mass M = 10 kg can slide with no friction along twoconducting rails separated by distance L = 0.5 m, as shown in the figure. Auniform 5 Tesla magnetic field points into the page, as indicated by crosses.An external force Fappis applied to the bar such that the velocity of the barin the x-direction as a function of time t is given by v = v0cos(ωt), wherev0= 4 ms and ω = π rad/s. What is the magnitude of the maximum inducedcurrent in the R = 0.5 Ohm resistor?x-axis(1) 20 Amps(2) 10 Amps(3) 5 Amps(4) 30 Amps(5) 40 Amps9. In the previous problem, at what time t (in s) is the induced current equal to zero?(1) 0.5 (2) 1 (3) 2 (4) 0 (5) never10. At time t = 0 s, the switch of an RL circuit consisting of a 12 V battery (EMF), a 0.5Ω resistor, and a 0.3 H inductoris closed. How long does it take the current in the circuit to reach 50% of its maximum value?(1) 0.42 s (2) 1.5 s (3) 0.11 s (4) 12 s (5) 4.1 s77777 7777711. Two wires each carrying a current of 2 A are placed in a uniform magnetic field. The wires make an angle of 40 degreeswith respect to each other. If the net force on one wire is zero and the other wire experiences a force of 5 N per meterof wire, what is the magnitude of the external magnetic field? Neglect forces due the magnetic field generated by thewires.(1) 3.9 T (2) 2.5 T (3) 1.6 T (4) 0.7 T (5) 8.2 T12. Which of the following four statements are true:(A) Electric fields are produced by charged particles.(B) Magnetic fields are produced by moving charged particles.(C) Electric fields are produced by magnetic fields that vary with time.(D) Magnetic fields are produced by electric fields that vary with time.(1) ABCD (2) ABD (3) ABC (4) only A and B (5) only A13. A light ray enters a rectangular glass slab (n = 1.5) at point A at an incidentangle θ and then undergoes total internal reflection at point B at the interfacebetween the glass and water (n = 1.3) as shown in figure. What is the maximumincident angle θ (in degrees) for this to occur?Glassn = 1.5AirABθWatern = 1.3(1) 48.5(2) 31.3(3) 23.6(4) 41.5(5) 62.814. A 5.0-ft