A P Physics C: Electricity and Magnetism 2014 Free …

1 AP Physics C: Electricity and Magnetism 2014 free -Response Questions 2014 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. Visit the College Board on the Web: AP Central is the official online home for the AP Program: TABLE OF INFORMATION, EFFECTIVE 2012. CONSTANTS AND CONVERSION FACTORS. Proton mass, m p = 10 -27 kg Electron charge magnitude, e = 10 -19 C. Neutron mass, mn = 10 -27 kg 1 electron volt, 1 eV = 10 -19 J. Electron mass, me = 10 -31 kg Speed of light, c = 108 m s Universal gravitational Avogadro's number, N 0 = 1023 mol-1. constant, G = 10 -11 m 3 kgis2. R = J (mol iK) Acceleration due to gravity Universal gas constant, at Earth's surface, g = m s2. Boltzmann's constant, k B = 10 -23 J K. 1 unified atomic mass unit, 1 u = 10 -27 kg = 931 MeV c 2.

2 Planck's constant, h = 10 -34 J is = 10 -15 eV is hc = 10 -25 J im = 103 eV i nm Vacuum permittivity, 0 = 10 -12 C2 N im 2. Coulomb's law constant, k = 1 4 p 0 = 109 N im 2 C2. Vacuum permeability, m0 = 4 p 10 -7 (T im) A. Magnetic constant, k = m0 4 p = 1 10 -7 (T i m) A. 1 atmosphere pressure, 1 atm = 105 N m 2 = 105 Pa meter, m mole, mol watt, W farad, F. kilogram, kg hertz, Hz coulomb, C tesla, T. UNIT. second, s newton, N volt, V degree Celsius, C. SYMBOLS. ampere, A pascal, Pa ohm, W electron-volt, eV. kelvin, K joule, J henry, H. PREFIXES VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES. Factor Prefix Symbol q 0 30 37 45 53 60 90. 10 9 giga G sin q 0 12 35 2 2 45 3 2 1. 106 mega M cos q 1 3 2 45 2 2 35 12 0. 103 kilo k tan q 0 3 3 34 1 43 3 . -2 centi c 10. The following conventions are used in this exam. 10 -3 milli m I.

3 Unless otherwise stated, the frame of reference of any problem is 10 -6 micro m assumed to be inertial. II. The direction of any electric current is the direction of flow of positive 10 -9 nano n charge (conventional current). 10 -12 pico p III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. -2- ADVANCED PLACEMENT Physics C EQUATIONS, EFFECTIVE 2012. MECHANICS Electricity AND Magnetism . u = u0 + at a = acceleration 1 q1q2 A = area F =. F = force 4 p 0 r 2 B = magnetic field 1 2 f = frequency C = capacitance x = x0 + u0 t + at 2 h = height F d = distance E=. I = rotational inertia q E = electric field u 2 = u0 2 + 2a ( x - x0 ) J = impulse e= emf Q. F = Fnet = ma K. k =. =. kinetic energy spring constant E i d A = 0 F =. I =. force current = length J = current density dp dV.

4 F= L = angular momentum E =- L = inductance dt dr m= mass = length J = F dt = Dp N = normal force q rii 1 n = number of loops of wire V =. P = power 4 p 0 i per unit length p = mv p = momentum N = number of charge carriers r = radius or distance 1 q1q2 per unit volume UE = qV = P = power F fric m N r = position vector 4 p 0 r T = period Q = charge Q q = point charge W = Fidr t =. U=. time potential energy C =. V R = resistance u = velocity or speed r = distance K =. 1 2. mu k 0 A t = time 2 W= work done on a system C =. d U = potential or stored energy x = position dW m= coefficient of friction Cp = Ci V= electric potential P= u =. dt q = angle i velocity or speed r= resistivity P = Fiv t = torque 1 1. = fm = magnetic flux w= angular speed Cs C. i i DUg = mgh a= angular acceleration k = dielectric constant f = dQ. phase angle I =.

5 U2 dt ac = = w2 r r Fs = - k x Uc =. 1 1. QV = CV 2 B i d = m0 I. t=r F 2 2. Us =. 1 2. kx m0 I d r 2 r dB =. t = t net = I a R= 4p r3. x = xmax cos( wt + f) A. I = r dm = mr 2 2. E = rJ. F= I d B. 2p 1. T = =. w f I = Neud A Bs = m0 nI. rcm = mr m u = rw Ts = 2 p m V = IR fm = B i d A. k L = r p = Iw Rs = Ri d fm Tp = 2p g i e = Eid = - dt 1 2. K = Iw 1. = R. 1. dI. 2 Gm1m2 Rp i i e = -L. FG = - r dt w = w0 + at r2. P = IV 1 2. Gm1m2 UL = LI. 1 2 UG =- 2. q = q0 + w0 t + at r FM = qv B. 2. -3- ADVANCED PLACEMENT Physics C EQUATIONS, EFFECTIVE 2012. GEOMETRY AND TRIGONOMETRY CALCULUS. Rectangle A= area df d f du =. A = bh C= circumference dx du dx V= volume Triangle S = surface area d n dx ( x ) = nxn -1. 1. A= bh b = base Circle 2 h = height d x dx (e ) = e x = length d A = pr2 w= width ( ln x ) = 1. r = radius dx x C = 2p r d Rectangular Solid (sin x ) = cos x dx V = wh d Cylinder (cos x ) = - sin x dx V = pr2 1.

6 X x n + 1 , n -1. n dx =. n +1. S = 2p r + 2p r 2. e x Sphere dx = e x 4 3 dx V =. 3. pr x = ln x S = 4p r 2. cos x dx = sin x Right Triangle sin x dx = - cos x a 2 + b2 = c2. a sin q = c a c q 90 . b cos q = b c a tan q =. b -4- 2014 AP Physics C: Electricity AND Magnetism free -RESPONSE QUESTIONS. Physics C: Electricity AND Magnetism . SECTION II. Time 45 minutes 3 Questions Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part. E&M. 1. Physics students are analyzing the circuit above. A variable DC power supply is connected to an ammeter and three resistors. The resistances of two of the resistors are known to be R2 = R3 = 50 W , but the resistance of the third resistor is unknown.

7 The students collect data on the potential difference across the power supply and the current measured by the ammeter, as follows. Potential Difference (V) 2 4 6 8 10. Current (mA) 40 55 97 138 155. (a) On the grid below, plot the data points for the current as a function of the potential difference. Clearly scale and label all axes, including units if appropriate. Draw a straight line that best represents the data. 2014 The College Board. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -5- 2014 AP Physics C: Electricity AND Magnetism free -RESPONSE QUESTIONS. (b) Using the straight line from part (a), calculate the total resistance of the three-resistor combination. (c) Calculate the value of R1 . The power supply is now fixed at 12 V. (d) Calculate the current through R2 . (e) Resistor 3 is now removed and replaced by an open switch in series with an uncharged 4 nF capacitor, as shown below.

8 The power supply is still fixed at 12 V. i. Calculate the current in R2 immediately after the switch is closed. ii. A long time after the switch is closed, will the magnitude of the current in R2 be greater than, less than, or equal to the current through R2 found in part (d) ? Greater than Less than Equal to Justify your answer. (f) The 4 nF capacitor is replaced with an uncharged 10 nF capacitor. Will the magnitude of the current in R2. immediately after the switch is closed be greater than, less than, or equal to the current in part (e)i ? Greater than Less than Equal to Justify your answer. 2014 The College Board. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -6- 2014 AP Physics C: Electricity AND Magnetism free -RESPONSE QUESTIONS. E&M. 2. The rectangular loop of wire shown on the left in the figure above has mass M, length L, width L 4 , and resistance R.

9 It is initially moving to the right at constant speed u0 , with no net force acting on it. At time t = 0. the loop enters a region of length 2L that contains a uniform magnetic field of magnitude B directed into the page. The loop emerges from the field at time t f with final speed u f . Express all algebraic answers to the following in terms of M, L, R, B, u0 , and fundamental constants, as appropriate. (a) Let x represent the position of the right end of the loop. Place a check mark in the appropriate box in each column in the table below to indicate whether the speed of the loop increases, decreases, or stays the same as the loop moves to the right. Position of Right End of Loop Speed of Loop L < x < 2L 2L < x < 3L 3L < x < 4L 4 L < x < 5L. Increases Decreases Stays the same (b) Derive an expression for the magnitude of the current induced in the loop as its right edge enters the field.

10 (c) What is the direction of the induced current determined in part (b) ? ____ Clockwise ____ Counterclockwise Justify your answer. (d) Write, but do not solve, a differential equation for the speed u as a function of time as the loop enters the field. (e) What is the direction of the acceleration of the loop just before its left edge leaves the field? ____ Left ___ Right ____ Up ____ Down Justify your answer. 2014 The College Board. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -7- 2014 AP Physics C: Electricity AND Magnetism free -RESPONSE QUESTIONS. E& A scientist describes an electrically neutral atom with a model that consists of a nucleus that is a point particle with positive charge +Q at the center of the atom and an electron volume charge density of the form - b e- r a r <a . r (r ) = r2. 0 r >a where a and b are positive constants and r is the distance from the center of the atom.