5/16/2014 TEST4 4BSP'14 l'tj~ rfhls

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1 5/16/2014 TEST4 4BSP'14 l'tj~ rfhls Throughout this examination the symbol for out is 0. Thesymbolforinis 8. SHOW ALL WORK. 1. ( 40 points) At some instant, two protons on "try out" at CERN's epochal experiment move in opposite directions horizontally. They travel relative to stationary midpoint P. The distanced is 8.00xlO - ls m -- on the order of a typical nuclear separation. The proton charge is e = 1.6xl 0-19 C. The upper proton moves half as fast as the lower one, which has nonrelativistic speed v = 9.00xlO 6 mis. e..., ,,...,,.. v /2 p d v / d e (a) (30 points) When the two charges are at the vertically displaced locations shown in the above figure, what are the DRECTON AND MAGNTUDE of the NET magnetic field they produce at P? (b) ( 4 points) What is the direction and magnitude of the magnetic force on the upper proton? ( c) (2 points) What is the direction and magnitude of the magnetic force on the lower proton? ( d) ( 4 points) f the upper proton's direction of motion were reversed, so both charges were moving in the same direction, what would be the direction and magnitude of the magnetic force on the upper proton? What's the direction and magnitude of the magnetic force on lower proton in that case? (e) EXTRA CREDT (4 PONTS) Using symbols, including k and µ 0, find the ratio of the magnitudes of the magnetic force over the electric force on upper proton. Which force has the larger magnitude, the electric or magnetic?

2 5/16/2014 TEST 4 4B SP' l ( 40 points) This problem deals with a sensitive current sensor based on detection of a magnetic field at a central location. Use symbols. Find the (a) ( 10 points) direction and (b) (26 points) magnitude of this magnetic field at point P due to the quarter-circular section of wire with current shown in the schematic of sensor. The circular-arc section has radius Rand point Pis at the center. (c) ( 4 points) Using and explaining a formula from Ch. 28, show that current in the long straight sections of the wire produce no field at P. p

3 5/16/2014 TEST 4 4B SP' (18 points) Current sensor based on a magnetic field due to straight wire section. A conductor of length 2L carries a current. Using symbols, find (a) ( 6 points) The direction and (b) (8 points) magnitude of the magnetic field at point P a distance x from the conductor on its perpendicular bisector. ( c ) ( 4 points) What is the answer to part (b) in the limit that L goes to infinity while distance x is held constant? P x

4 5/16/2014 TEST 4 4B SP' l (40 points) nside a damaged control panel on the Star Federation Ship Enterprise, two horizontally displaced long parallel wires have currents flowing as shown. The wires are perpendicular to the page. The distance between the wires is d = m. The current A in wire A is 9.00 (A) OUT. The current 8 in wire Bis 9.50 (A) N. Figure 2 is for part ( d). Note: µ 0 = 1.257x10-6 T m/a = 4n10-7 T m/a. For parts (a), (b), (c) see figure 1; for part (d), figure 2. (a) (20 points) What is the magnitude of the net magnetic field due to both wires at midpoint P of the perpendicular segment between wires? (b) (10 points) What is the direction of the net magnetic field due to both wires at midpoint P? (c) (6 points) What is the magnitude and direction of the magnetic force on a 1.00 m section of wire B due to the magnetic field of wire A? (d) (4 points) n figure 2, a point particle with negative charge q at midpoint P between wires moves with velocity OUT OF PAGE. What is the (i) direction and (ii) magnitude of the force on the charge at that moment, assuming q = -1.4x10-6 (C) and speed v = 2.00xlO 6 mis. p 1 A 8---~~ ~ ~~~~-@ 1e figure 1 '1 p 1 A G f f@ Q'.?Pe 1'

5 5/16/2014 TEST 4 4B SP'l (35 points) A single circular loop of radius r = 1.0 mis placed in a region where a uniform magnetic field is perpendicular to the loop's plane. The magnetic field vector points in. While the vector points in, the magnitude B of the magnetic field is allowed to change linearly with time t according to the equation: B = B t ( T), where time tis in seconds. Assume at time t the expression for B is positive and the vector B points in. B 0 is the value of the changing magnitude B at time t = 0. (a) (10 points) What is the direction of the induced current in the loop, clockwise or counterclockwise, for t ~ 0? Please indicate this direction by drawing an arrow at the wire. Explain your reasoning. (b) (10 points) What is the direction of the induced magnetic field vector -BiHn, in or out, for t "2. O? Please indicate this direction by drawing a symbol within the loop boundary. Explain your reasoning. (c) (10 points) Calculate the magnitude of the induced emf (in volts) for t;;:: O. (d) (5 points) Suppose the loop has a resistance R = o. What would be the value of the induced current for t 2: O? 8-vector in wire loop

6 5/16/2014 TEST 4 4B SP' EXTRA CREDT. 12 PONTS. LR series circuit with current build up. An inductor with an inductance L = 2.50 Hand a resistor with R = 8.00 ohms are connected in series to the terminals of a battery with an emf of 6.00 (V). The switch connecting these three series elements is closed at t = 0 and the current begins to increase from its initial value of zero. Find: (a) (3) the initial rate of change of the current in the circuit. (b) (3) the rate of change of the current when the current is (A) ( c ) (3) the current seconds after the switch is closed ( d) (3) the final steady state current after a very long time.

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