Physics 102 Final Exam Spring 2004c = 3x108 m/s; h = 6.63x10-34 J.s; k = 9x109 N.m2/C2e = 1.6x10-19 C; me = 9.1x10-31 kg;o = 8.85x10-12 F/m; µo = 1.26x10-6 = 4πx10-7 T.m/A1. (20 points) A charge Q1 = +4.2 µC is at x = 0 and a charge Q2 = -2.9 µC is at x = 0.37 m.a. What is the electric potential at x = 0.75 m?b. What is the electric field (magnitude and direction) at x = 0.75 m?c. An electron is placed, at rest, at x = 0.75 m. When released will it be accelerated in the +x or the -x direction?d. What is the electron's speed after travelling 0.30 m?b. Indicate on the diagram the direction of B.c. Find the magnitude of the magnetic force exerted on wire 1 by wire 2.d. Is this force attractive or repulsive?dER3R2R12. (20 points) R1 (wire 1) and R2 (wire 2) are long (L = 1.5 m), straight, parallel wires separated bya distance d = 0.09 m. The current through R1 is 4.1 A; the current through R2 is 3.4 A. R1 = 0.34 .a. Find the magnitude of the magneticfield B produced by wire 2 at the position of wire 1.e. Wire 1 is made of aluminum, which has a resistivity of 2.82x10-8 .m. What is the radius of wire 1?f. Find R2.g. If R3 = 0.47 , find the total resistance of the circuit.h. Find E, the EMF of the battery.a. the magnetic field produced by the solenoid.b. the magnetic field produced by the coil at its center.c. the total magnetic field at the center of the coil.I1I23. (20 points) A 3500 turn solenoid with a length 0.45 m and radius 0.03 mcarries a counterclockwise current I1 = 0.67 A. Inside the solenoid there is a 75 turn, flat coil with a radius of 0.015 m. The coil carries a counterclockwise current I2 = 0.83 A. The coil and the solenoid are coaxial.Findd. the magnetic moment of the coile. the potential energy of the coil in the field of the solenoid.f. the magnitude of the torque exerted on the coil by the field of the solenoidg. If I1 is suddenly decreased to zero, will the current induced in the coil be parallel to or opposite the direction of I2? Explain youranswer carefully.4. (10 points) Light of wavelength 485 nm travels in air toward a metal sheet in which a rectangular slit of width 4500 nm has been etched.a. Some of the light passes through the slit and strikes a wall that is 0.65 m beyond the slit. What is the width in meters of the centralmaximum of the diffraction pattern produced on the wall?b. What is the momentum of a photon of this wavelength?c. Some of the light strikes the metal and ejects photoelectrons with a maximum kinetic energy of 1.7x10-19 J. What is the work function ofthe metal in eV?5. (15 points) A beam of electrons is accelerated from rest through a potential difference V. They then travel with a speed v = 1.7x107 m/s into a perpendicular magnetic field of 5.6 mT.a. What is the radius of curvature of the electron beam in the magnetic field?b. What is the de Broglie wavelength of the electrons in the beam?c. The electrons were accelerated to that speed by a uniform electric field E applied over a distance d = 0.025 m. Find E.d. Comment on the concept of "wave-particle duality" for matter based on this situation.6. (5 points) Explain carefully how you would determine the radius of curvature of a convex mirror (e.g., convenience store security mirror)from an analysis of the image it produces.a. Find d.b. The index of refraction of the plastic was determined in a prior experiment. Light was directed through the ITO toward the plastic atan angle of incidence in the ITO of 48o. What was the angle of refraction of the light in the plastic?c. ITO is very useful in modern technology because it is transparent to visible light, yet is a good conductor of electricity. Hence, the ITO on either side of the plastic can serve as capacitor plates. If each ITO layer has an area of 4x10-4 m2 in contact with the plastic and the dielectric constant of the plastic is 6, what is the capacitance of the system shown in the figure? PlasticdlightITOITO7. (10 points) A new plastic is being evaluated for its applicability as a dielectric forthin-film capacitors. To determine the thickness of the plastic sheet it is placed between two layers of Indium Tin Oxide (ITO), for which n = 1.95. Suppose that for the plastic n = 2.40. Light is shone on the surface as illustrated in the diagram. Maximum reflection is observed for  (in air) of 550