Name. Physics 111. Winter Exam #2. February 10, Part Multiple Choice / 12 Problem #1 / 24 Problem #2 / 32 Problem #3 / 32 Total / 100

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1 Physics 111 Winter 010 Exam # February 10, 010 Name In keeping with the Union College policy on academic honesty, it is assumed that you will neither accept nor provide unauthorized assistance in the completion of this work. Part Multiple Choice / 1 Problem #1 / 4 Problem # / 3 Problem #3 / 3 Total / 100

2 Part I: Free Response Problems Please show all work in order to receive partial credit. If your solutions are illegible or illogical, no credit will be given. Please use the back of the page if necessary, but number the problem you are working on. 1. Consider the circuit below in which you have a collection of resistors, in which all eleven resistors have a value of 100Ω and are connected in various combinations to a 1V battery. a. What are the equivalent resistance of the circuit and total current produced by the battery? R & R 3 in series R 3 = 00Ω R 5 & R 6 in series R 56 = 00Ω R 7 & R 8 in series R 78 = 00Ω R 9 & R 10 in series R 910 = 00Ω R 910 in parallel with R 78 R = 100Ω R 11, R 56, & R in series R = 400Ω R 3 in parallel with R R = 133.3Ω R 1, R , R 4 in series R eq = R = 333.3Ω The total current is I total = V R eq = Therefore we have P 1 = I total 1V = 0.036A = 36mA 333.3Ω R 1 = ( 0.036A) 100Ω = 0.17W =17mW ; V 1 = V 4 = I total R 1 = 0.036A 100Ω = 3.6V ; V = V 3 = V = I total R = 0.036A 133.3Ω = 4.8V ; I = V 3 = 4.8V R 3 00Ω = 0.04A = 4mA; I = V = 4.8V R Ω V = V 3 = I R = 0.04A 100Ω =.4V ; V 5 = V 6 = V 11 = V = V 910 = V 78 = I 1 R 5 = 0.01A 100Ω =1.V ; I 3 = I 4 = V 910 = V 78 = 1.V = 0.006A = 6mA; R 910 R 78 00Ω V 7 = V 8 = V 9 = V 10 = I 4 R 7 = 0.006A 100Ω = 0.6V = 0.01A =1mA b. What are V 9,10 and I? I = 0.04A = 4mA; V 910 = 1.V c. What are V, I 4, and P 1? V =.4V; I 4 = 0.006A = 6mA; P 1 = 0.18W=17mW

3 . A metal rod having a mass of 0.005kg and length of 1.0m carries a current of I = 5.0A. The rod hangs from two massless wires in a uniform magnetic field B. The rod hangs vertically in equilibrium (when no current flows) and when current I flows, the wire feels a magnetic force and swings to an angle θ measured with respect to the vertical. a. What are the directions of the magnetic force and magnetic field needed to produce this effect? Explain your answer fully in order to receive partial credit. Since the rod moves to the left, the force must be to the left. Therefore the magnetic field, by the right hand rule has to point vertically up the page. Face-on view I θ Side view b. What is the magnitude of the magnetic force needed to produce this effect if the wires make an angle of θ = 45 o with respect to the vertical? F X : F T sinθ F B = 0 F B = F T sinθ = 0.035N sin45 = 0.049N = 49mN F y : F T cosθ mg = 0 F T = mg cosθ = 0.005kg 9.8 m s cos 45 = 0.035N c. What is the magnitude of the magnetic field? F B = ILB B = F B IL = 0.049N = T = 9.8mT 5A 1m d. Suppose that the magnetic field in part c were actually produced using a current flowing in another nd wire located m away from this suspended wire. What are the two possible orientations of this second wire be and what current (magnitude and direction) would be flowing in each orientation of the second wire to generate the magnetic field direction in part a? The orientations are parallel to the given wire either on the left of the given wire or on the right. If the wire is on the left then the current is directed out of the page (or parallel to the current in the wire) so to produce an attractive force by the right hand rule. If the wire is on the right then the current is directed into the page (or antiparallel to the current in the wire) so to produce a repulsive force by the right hand rule. The magnitude of the current is given as: B = µ o I wire πr I wire = πrb µ o = π m T 4π 10 7 TM A = 98000A

4 3. Suppose that you have the mass spectrometer shown below, in which you have a sample of unknown ions that are accelerated from rest through a potential difference of ΔV = 100kV and enter into a region of space, defined by the dashed box, in which the magnetic field has strength B = 5T in the indicated direction. a. Ions of which charge strike the upper plate? the lower plate? Explain your answer fully for partial credit. By the right hand rule, a positive ion will strike the upper plate, and a negative charge will strike the lower plate since the velocity of the charge is directed to the right and the magnetic field points into the page. b. Suppose that your sample contained singly charged positive ions each of a different chemical species. If the orbital radius is 84mm for species #1 and 105mm for species #, derive an expression for the ratio of the mass of species # to the mass of species #1 and then evaluate your expression using the information given. F B = ma c qvb = m v r r = mv qb r = m v q B = m q B r 1 = m V 1 and r qb = m V m = r qb m 1 r = 105mm 1 84mm m =1.56m 1 qv m =1.56 = mv qb c. Suppose instead that your sample contained K +1 ions and another ion of unknown mass but that you knew that ion with unknown mass had a + charge. What is the mass (in amu) of the ion with the + charge if the potassium ion has a mass of 39amu an orbital radius of r K = 56.9mm and the unknown ion had an orbital radius of r unk = 40.7mm? Using the results from part b, r K = m V K and r qb unk = m V unk m unk = r unk qb m K r K m unk =1.0m K =1.0 39amu = 40amu out to be calcium ions. = 40.7mm 56.9mm =1.0 which turns d. Lastly, suppose that your sample contained Cl - ions. What would the time of flight of the Cl - ions be in the magnetic field? (That is, how long would it take for the Cl - ion (of mass 35amu) to strike a plate if time t i = 0 when the Cl - ion first enters the field from the accelerator.) F B = qvb = m v r v = πr t = qbr m t = πm qb π 35amu 7 kg 1amu = C 5T = s

5 Part II: Multiple-Choice Circle the best answer to each question. Any other marks will not be given credit. Each multiple-choice question is worth 3 points for a total of 1 points. 1. Suppose that you have the three rectangular loops of wire (seen edge on) in the figure below. Which loop of wire experiences the greatest torque if they are all the same size and carry the same current? a. Loop a. b. Loop b. c. Loop c. d. Since they are all the same size and carry the same current, they all experience the same torque.. Suppose that you have two light bulbs with resistances R 1 and R. If a piece of wire is used to connect point b to point c in the figure below, the brightness of light bulb R 1 a. increases because the effective resistance increases. b. decreases because the effective resistance decreases. c. increases because the effective resistance decreases. d. decreases because the effective resistance increases. d. remains the same because the brightness of the bulb is independent of the current and resistance. 3. As an airplane is flying from Albany, NY to Calabria, Italy (in a due East direction) it passes through the Earth s magnetic field, which has a vertically downward component. Which of the following is true? a. The left wingtip is positively charged. b. The right wingtip is positively charged. c. The top of the plane is positively charged. d. The bottom of the plane is positively charged. 4. The game of could the answer be D? The physics department s administrative assistant secretly runs the entire department. (So don t tell anyone!) Her office hours are a. M F: 7 am 3 pm. b. M F: 8 am 4 pm. c. M F: 9 am 5 pm. d. Whenever she wants, after all she runs the department!

6 Electric Forces, Fields and Potentials Electric Circuits Light as a Wave Magnetic Forces and Fields Constants Light as a Particle Nuclear Physics Misc. Physics 110 Formulae Geometry