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Physics 2220 Spring 2012 Ben Bromley EXAM 2 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) x x 2 a 2 dx 1 3 x2 a2 3 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 dx x2 a2 3 x a2 x2 a2 1 year = 365.25 days ax e dx 1 kg = 0.0685 slug 1 N = 0.225 pound 1 horsepower = 550 ftڄpounds/s (exact) 24 Mearth = 5.98 × 10 kg Rearth = 6.38 × 103 km Msun = 1.99 × 1030 kg Rsun = 6.96 × 108 m 22 Mmoon = 7.35 × 10 kg Rmoon = 1.74 × 103 km G = 6.67 × 10-11 Nڄm2/kg2 9 2 2 k = 8.99 × 10 Nڄm /C εo = 8.85 × 10-12 F/m eelectron charge = -1.60 × 10-19 C melectron = 9.11 × 10-31 kg μo = 4π × 10-7 Tڄm/A (exact) N(Avogadro's No.) = 6.02 × 1023 atoms/gmڄmole 26 = 6.02 × 10 atoms/kgڄmole cos(a ± b) = cos a cos b טa sin b xdx x2 a 2 3/2 xdx a2 x2 1 x2 a2 a2 x2 dx n x x 2 a 2 x2 a2 1 a x 2 a 2 n a x x x2 a2 dx x a x x sin 1 , or cos 1 a a a2 x2 xdx 2 2 x2 a2 dx 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 1 Tesla = 10,000 gauss (exact) ρ(H2O) = 1000 kg/m3 1 eax a dx 1 n a bx a bx b dx a bx 2 1 b a bx Physics2220 2220 Physics Spring 2012 Fall 2009 Ben Bromley Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 2 1 Show all work!! Report all numbers to three (3) significant figures. A. A uniform electric E 4.5iˆ N / C exists in a region of space containing 3 points: O (at the origin), A (0.4, 0) m and B at (0.4, 0.3 m). Find the change in electric potential ΔVif for the following paths: ΔVOA ______________________ (path from O to A) ΔVAB ______________________ ΔVBO ______________________ ΔVloop ______________________ (loop from O to A to B to O) B. The electric potential relative to a point at the origin is V(x,y.z) = V1x + V2z2. Find the electric field E (x, y, z). (Use unit vector ˆi, ˆj, kˆ , as needed). PhysicsPhysics 2220 2220 Fall 2009 Spring 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 2 Show all work!! Report all numbers to three (3) significant figures. A. Two concentric conducting shells have radii a and b (a < b) as shown. The shells may be treated as if they were a pair of conductors within a single capacitor of capacitance C. Find C. Must show all work and justify your answer. B. For the circuit shown, find I3, the amount of current through the 3 Ω resistor (labeled R3). ε1 = 6 V; ε2 = 6 V; R1 = 2 Ω; R2 = 2 Ω; R3 = 3 Ω Ben Bromley 2 Physics2220 2220 Physics Spring 2012 Fall 2009 Ben Bromley Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 2 3 Show all work!! Report all numbers to three (3) significant figures. In a model for a thunderstorm, we might view the Earth’s surface and the lower face of the storm cloud as parallel plates of a capacitor, with capacitance C = 1.2 μF. The model storm is driven by an emf ε = 2.4 MV (to account for the energy input from the Sun, and the convection in the clouds). The system also has some resistance R = 150 MΩ (associated with moving charges around the system). (a) If the surface area of the storm cloud’s lower face is 25 km2 = 2.5 × 107 m2, what is the distance d between the Earth and the clouds, assuming the system acts like a perfect parallel plate capacitor? d = __________________ (b) What is the maximum charge Q that can be exchanged between the Earth and clouds in this model? Q = ___________________ (c) Find the time T required to build up a voltage ΔVC = 1.2 MV across the capacitor. T = ____________________ (d) If at some point some amount of charge, q = 0.72 C is able to cut a path between the Earth and cloud (no one knows exactly how this process works), then lightning strikes. If the lightning bolt is approximated as a uniform column of charge of length L = 300 m and radius r = 76 mm, flowing at a steady rate for a duration of 30 μs, find the current density J in the lightning bolt and the total current I. J = ____________________, I = ____________________