2002 Electricity

2002 Electricity - Physics C: Electricity and Magnetism...

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Unformatted text preview: Physics C: Electricity and Magnetism TABLE OF INFORMATION FOR 2002 UNITS CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit, 1 u = 1.66 ™ 10 -27 = 931 MeV/c Proton mass, PREFIXES Name Symbol meter kilogram Factor Prefix Symbol m 10 9 giga G kg 10 6 mega M 10 3 kilo k kg 2 m p = 1.67 × 10 −27 kg Neutron mass, mn = 1.67 × 10 −27 kg second s Electron mass, me = 9.11 × 10 −31 kg ampere A 10 −2 centi c Magnitude of the electron charge, e = 1.60 × 10 −19 C kelvin K 10 −3 milli m micro µ Avogadro’s number, N0 = 6.02 × 10 mol 23 −1 mol hertz Hz 10 −9 nano n 10 −12 pico p Boltzmann’s constant, k B = 1.38 × 10 −23 J / K Speed of light, c = 3.00 × 10 8 m / s newton N Planck’s constant, h = 6.63 × 10 −34 J ⋅ s pascal Pa = 4.14 × 10 −15 eV ⋅ s Vacuum permittivity, Coulomb’s law constant, Vacuum permeability, Magnetic constant, Universal gravitational constant, Acceleration due to gravity at the Earth’s surface, 1 atmosphere pressure, 0 k = 1 / 4π = 8.85 × 10 C / N⋅m 0 k = µ 0 / 4π = 10 (T ⋅ m ) / A G = 6.67 ™ 10 -11 m 3 / kg ¼ s 2 g = 9.8 m / s V Ω H farad −7 0 henry µ 0 = 4π × 10 −7 (T ⋅ m ) / A C ohm = 9.0 × 10 N ⋅ m 2 / C 2 θ volt 9 W coulomb 2 J watt = 1.24 × 10 3 eV ⋅ nm 2 VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES joule hc = 1.99 × 10 −25 J ⋅ m −12 10 mole R = 8.31 J / ( mol ¼ K ) Universal gas constant, −6 F tesla T 45o o = 1.0 × 10 Pa tan θ 0 1 0 3 /2 3 /3 1/2 37o 3/5 degree Celsius o C 53o eV 60 o 90o 1 atm = 1.0 × 10 5 N / m 2 cos θ 30o electronvolt 2 sin θ 2 /2 4/5 4/5 2 /2 3/4 1 3/5 4/3 3 /2 1/2 3 1 0 ∞ 5 1 electron volt, 1 eV = 1.60 × 10 −19 J The following conventions are used in this examination. I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current). 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 FOR 2002 MECHANICS a = acceleration F = force 1 x = x 0 + u 0 t + at 2 f = frequency 2 h = height 2 u 2 = u 0 + 2a x - x 0 I = rotational inertia Ê F = Fnet = ma J = impulse K = kinetic energy dp F= k = spring constant dt l = length J = F dt = Dp L = angular momentum p = mv m = mass N = normal force F fric ˆ mN P = power W = F dr p = momentum 1 2 r = radius or distance K = mu 2 r = position vector dW T = period P= dt t = time P=F v U = potential energy u = velocity or speed DUg = mgh W = work done on a system u 2 = w2r x = position ac = r m = coefficient of friction t=r™F q = angle Ê t = t net = Ia t = torque 2 2 w = angular speed I = r dm = Ê mr a = angular acceleration rcm = Ê mr Ê m u = rw L = r ™ p = Iw 1 K = Iw 2 2 w = w0 + at q = q 0 + w0 t + 1 at 2 2 Fs = - kx 1 Us = kx 2 2 2p 1 T= = f w m Ts = 2 p k l Tp = 2 p g Gm1m2 $ FG = r r2 Gm1m2 UG = r u = u 0 + at 0 I I I œ 5 ELECTRICITY AND MAGNETISM q1 q 2 A = area 2 B = magnetic field r 0 C = capacitance F d = distance E= q E = electric field e = emf Q E • dA = F = force 0 I = current dV L = inductance E=− l = length dr n = number of loops of wire per qi 1 V= unit length 4 p 0 i ri P = power 1 F= 4p ∑ UE = qV = 1 4p 0 q1 q 2 r Q C= V kA C= 0 d C p = ∑ Ci i 1 1 =∑ Cs i Ci dQ dt 1 1 Uc = QV = CV 2 2 2 rl R= A V = IR I= Rs = ∑ Ri i 1 1 =∑ Rp i Ri P = IV FM = qv × B B • d ø = m0 I I F = I dø × B Bs = m0 nI I fm = B • dA dfm dt dI e = −L dt 12 U L = LI 2 e=− 3 Q= q= R= r= t= U= V= υ= r= fm = k= charge point charge resistance distance time potential or stored energy electric potential velocity or speed resistivity magnetic flux dielectric constant ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2002 GEOMETRY AND TRIGONOMETRY Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2 pr Parallelepiped V = lwh Cylinder V = pr 2 l S = 2 prl + 2 pr 2 Sphere 4 V = pr 3 3 S = 4 pr 2 Right Triangle a 2 + b2 = c2 a sin q = c cos q = area circumference volume surface area base height length width radius c q a 90 b b c tan q = A= C= V= S= b= h= l= w= r= a b CALCULUS df d f du = dx du dx 27 27 dn n -1 x = nx dx dx e = ex dx d 1 (1n x) = dx x d (sin x) = cos x dx d (cos x) = - sin x dx 1 n +1 xn dx = x , n ž -1 n +1 e x dx = e x I I I dx = 1n x x cos x dx = sin x I I sin x dx = - cos x 4 2002 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS PHYSICS C Section II, ELECTRICITY AND MAGNETISM 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 the pink booklet in the spaces provided after each part, NOT in this green insert. E&M 1. A rod of uniform linear charge density l = +1.5 ™ 10 -5 C m is bent into an arc of radius R = 0.10 m. The arc is placed with its center at the origin of the axes shown above. (a) Determine the total charge on the rod. (b) Determine the magnitude and direction of the electric field at the center O of the arc. (c) Determine the electric potential at point O. A proton is now placed at point O and held in place. Ignore the effects of gravity in the rest of this problem. (d) Determine the magnitude and direction of the force that must be applied in order to keep the proton at rest. (e) The proton is now released. Describe in words its motion for a long time after its release. Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 5 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 2. Your engineering firm has built the RC circuit shown above. The current is measured for the time t after the 05 switch is closed at t = 0 and the best-fit curve is represented by the equation I t = 5.20 e -t / 10 , where I is in milliamperes and t is in seconds. (a) Determine the value of the charging voltage V0 predicted by the equation. (b) Determine the value of the capacitance C predicted by the equation. (c) The charging voltage is measured in the laboratory and found to be greater than predicted in part (a). i. Give one possible explanation for this finding. ii. Explain the implications that your answer to part i has for the predicted value of the capacitance. (d) Your laboratory supervisor tells you that the charging time must be decreased. You may add resistors or capacitors to the original components and reconnect the RC circuit. In parts i and ii below, show how to reconnect the circuit, using either an additional resistor or a capacitor to decrease the charging time. i. Indicate how a resistor may be added to decrease the charging time. Add the necessary resistor and connections to the following diagram. ii. Instead of a resistor, use a capacitor. Indicate how the capacitor may be added to decrease the charging time. Add the necessary capacitor and connections to the following diagram. Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 6 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS E&M 3. A circular wire loop with radius 0.10 m and resistance 50 W is suspended horizontally in a magnetic field of magnitude B directed upward at an angle of 60• with the vertical, as shown above. The magnitude of the field in teslas is given as a function of time t in seconds by the equation B = 4(1 – 0.2t). (a) Determine the magnetic flux fm through the loop as a function of time. (b) Graph the magnetic flux fm as a function of time on the axes below. Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 7 GO ON TO THE NEXT PAGE. 2002 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS (c) Determine the magnitude of the induced emf in the loop. (d) i. Determine the magnitude of the induced current in the loop. ii. Show the direction of the induced current on the following diagram. (e) Determine the energy dissipated in the loop from t = 0 to t = 4 s. END OF SECTION II, ELECTRICITY AND MAGNETISM 8 ...
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