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Physics 2220 Spring 2012 Ben Bromley FINAL EXAM PLEASE FILL IN THE INFORMATION BELOW Name (printed): Name (signed): Student ID Number Discussion Instructor: U __ __ __ __ __ __ __ Chad Jon Paul Maria Peter Physics 2220 Spring 2012 Ben Bromley Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes). 1 ft = 12 in (exact) 1 m = 3.28 ft 1 mile = 5280 ft (exact) 1 hour = 3600 sec = 60 min (exact) 1 day = 24 hr (exact) 2 2 gearth = 9.80 m/s = 32.2 ft/s gmoon = 1.67 m/s2 = 5.48 ft/s2 1 year = 365.25 days 1 kg = 0.0685 slug 1 N = 0.225 pound 1 horsepower = 550 ftڄpounds/s (exact) Mearth = 5.98 × 1024 kg 3 Rearth = 6.38 × 10 km Msun = 1.99 × 1030 kg Rsun = 6.96 × 108 m Mmoon = 7.35 × 1022 kg Rmoon = 1.74 × 103 km G = 6.67 × 10-11 Nڄm2/kg2 k = 8.99 × 109 Nڄm2/C2 x melectron = 9.11 × 10-31 kg μo = 4π × 10-7 Tڄm/A (exact) N(Avogadro's No.) = 6.02 × 1023 atoms/gmڄmole = 6.02 × 1026 atoms/kgڄmole 1 Tesla = 10,000 gauss (exact) ρ(H2O) = 1000 kg/m3 cos(a ± b) = cos a cos b טa sin b sin(a ± b) = sin a cos b ± sin b mproton = 1.67 × 10−27 kg h = 6.64 × 10-34 J π = 3.14 8 c = 3.00 × 10 m/s dx x 2 a 2 3/2 ax e dx εo = 8.85 × 10-12 F/m eelectron charge = -1.60 × 10-19 C x 2 a 2 dx 1 3 x2 a2 3 x a2 x2 a2 1 eax a xdx x2 a2 xdx a2 x2 3/2 1 x2 a2 a2 x2 dx n x x 2 a 2 x2 a2 1 a x2 a2 n a x x x2 a2 dx x2 a2 x x sin 1 , or cos 1 a a a2 x2 xdx x2 a2 dx dx 1 n a bx a bx b dx a bx 2 1 b a bx Physics2220 2220 Physics Spring 2012 Fall 2009 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Show all work!! Report all numbers to three (3) significant figures. A. A parallel plate capacitor has two oppositely charged sheets separated by a distance d, and containing a vacuum (see diagram above). The capacitor is charged to V = 12 V. An electron is placed at rest immediately to the inside of the negatively charged sheet. I t is then released, accelerating toward the positively charged sheet. What is the speed v of the electron when it reaches the positively charged sheet? [Hint: Don’t Force this one and it will Work out better….] V = __________________________ B. A spherically symmetric cloud of charge contained in a sphere of radius R has a volume charge density = +A/r2, where A is a constant and r < R is the distance from the center of the cloud. Find electric field E at a radius r = R/2. E = _________________________ Ben Bromley 1 PhysicsPhysics 2220 2220 Fall 2009 Spring 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Ben Bromley 2 Show all work!! Report all numbers to three (3) significant figures. A. A particle of mass m = 0.01 kg and charge q = 0.008 C has a velocity ˆ . It is observed to travel v 1.2iˆ 1.6ˆj m/s in a uniform magnetic field B 0.75kT in a circular path of radius R. Find that radius. R = _____________________________ B. Based on the figure shown, find the infinitesimal element of magnetic field dB at the point P (distance a above the x-axis), from the current I (flowing along the x-axis) through an element of length dx. Give your answer in terms of a and variable x. dB magnitude:_______________________, direction [+x,-x,+y,-y, in/out of page]:____________________ Find the B-field, Bsegment from a wire segment of length 2a, at a distance a from the center of the segment. [Hint: integrate your result for dB from x = -a to a.] Bsegment (magnitude):____________________ Finally, find the strength of the magnetic field at the center of a square wire loop (length 2a to a side, carrying current I) in terms of Bsegment: Bsquare (magnitude)_____________________ Physics2220 2220 Physics Spring 2012 Fall 2009 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Show all work!! Report all numbers to three (3) significant figures. A. A square wire loop (length A to a side) has a resistor with resistance R on one leg, and it travels with speed v to the right, as shown. At time t = 0 it crosses into a small, square region (length a to a side) which contains a uniform magnetic field of strength B and oriented perpendicular to the square wire loop. What is the power P dissipated through the resistor immediately after t = 0, when the larger loop is moving into the smaller square region? P = _____________________________ B. Find the three currents, I1, I2, and I3, in the circuit shown. I1 = ________________ I2 = ________________ I3=_________________ Ben Bromley 3 Physics2220 2220 Fall 2009 Physics Spring 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Ben Bromley 4 Show all work!! Report all numbers to three (3) significant figures. A. Coherent light of wavelength travels inside two optical fibers. The length of the straight fiber is L, while the other fiber has two straight segments of total length L plus a circular segment of radius R in between (see figure). If the light entering both fibers is in phase, what is the condition in terms of (L, R, , as needed) for constructive interference when the light coming out of the ends of the fibers is recombined? (Assume that light is a plane wave traveling along the axis of the wire, even if the wire is not straight.) B. In the optical/thin lens set-up shown, find the image location (relative to the first lens), orientation and height. Image location (distance left of right of lens)_______________________ Image orientation (upright or inverted)______________________ Image height________________________