midterm exam 2 solution

Physics for Scientists and Engineers (3rd Edition)

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Unformatted text preview: Problems: 1) The switch S in the circuit shown is closed for a long time, and then it is opened at t = 0. The values ofthe elements in the circuit are V = 6.0 V, R = 2.0 Q, C = 4.0 uF, L = 2.5 mH. i ' a) What is the current through the resistor R 3 1 just before the switch is opened? :DC (Zinc/wi‘i' 1M A‘IC«X\ {Sink V C =) m0 (Mn/nevi [zawmd C L gal/4A Will/LC M V — -— .0 :) V=VPJ0 :DLLOIS Q : m": 3.0/4 H b) What is the current through the inductor just after the switch is opened? SW,“qu OWA => 99m Cum/94+ lflrle Li c) What is the frequency of the oscillatiOn of the circuit? 1 (,0: 2T). = —"— F 4‘ LC' \ :: E ‘ - C :1 NE" 271’ 9.9 104123 >< LLO><IO V d) How much energy is stored in the capacitor at t = 0? L1 I 1 ? - VC 5) UC E :g L\ e) How much energy is stored in the inductor at t = 0? —-Z - .3 Z"! -2] M: 1L; :é—XZAXW IZSxGUDA «HXIO :{ 2 2) A solenoid with N = 200 turns ofwire has a radius r = 0.5 m and a length 1 = 2.0 m. It carries a current of I = 100 A. 5 a) What is the magnetic field inside this coil? — fl/ .1: : I :_ _..._..._.—r 3’ /Ao M /M 0 K _- ... c1141 200xt00,4_ 2, f0.3i EL”qu AX 2.0/w. "'Gx b) A charged particle with q = 10'3 C travels with a velocity of v = 10 m/s along the axis of j the coil. Determine the magnitude and the direction of the force on the particle when it is in the center of the coil. c) What is the self inductance of the coil? 3/ L:&:fl/ET/r2 '—u—- J- L 1—- ” 2 0xl2‘éxlofljxhx 0.25% L :5 20 t: d) How much energy is stored in the coil? 3/ 8 IE: % LI zél-XEOXlO’RIZrX [OH/4 :IUJOJI 3) A long wire along the z axis carries a current in the +2 direction. A rectangular coil with N = 4 turns and an area of A = 5 cm2 is placed on the +x axis with the plane of the coil in the x-z plane (see the diagram). To simplify the calculation use the approximation that the field at every point of the coil is the same as at the center of the coil, which is at x = +10 cm. a) What is the magnetic flux through the coil in terms of N, I, x, and A? “-" *3 b) If the current increases at a rate of 10 A/s, what is the absolute value of the voltage 6 induced in the 002i? 0 A44 ol I IE: "31433):% X 0H: :)|El:EXiO‘17g/Efl X c) In which direction will the induced current flow, clockwise or counterclockwise, while L! viewing the coil as shown in the diagram? Indicate this direction by drawing an arrow inthe diagram. ~ (gm-Z ‘ 3 M => ICOM/‘aL/vizzgwih‘} d) If the coil is rotated by 900 around the x axis so that it lies in the x-y plane, what will be the induced volta e 'usti our answer ? 2 a (J fy y ) 3 L0 213:”) «II/Um»; 4) Two long parallel wires, carrying currents of I; = 5.0 A and [2 = 10.0 A in opposite directions, are separated by a distance of d = 0.50 m as indicated in the sketch. a) Using Ampere’s Law, determine the magnetic field strength B at a point P located on the 10.0 A :2, wire due to the 5.0 A current’iir'fhe other wire. .— ( _ \ A “i/Pafl’d‘i/MWZ ( ‘ls \l A d - x / 5L8 Uh}; 3.01,? :3x2n =/u0._.| :> u AMOMJ (Lin/oz? a.) iflxrj/rCfi/‘iidi :> [E]:— ?X (Zigaxg’O/i :lEUx [0— Ti b) Calculate the resulting magnetic force per unit length on the 10.0 A wire and its direction. 1 -—— ~——- "“ - .— L“... +:_La,€3 => .1"; Egon/4&9“ .1200 ,W. you have calculated in parts a and b of this problem. X“ 390% 6 0) Draw arrows in the sketch to indicate the direction of the magnetic field and the force ...
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