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Unformatted text preview: AP Physics C: Electricity and Magnetism 2008 FreeResponse Questions The College Board: Connecting Students to College Success
The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,000 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,500 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its bestknown programs are the SAT, the PSAT/NMSQT, and the Advanced Placement Program (AP). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. 2008 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. TABLE OF INFORMATION FOR 2008 and 2009 CONSTANTS AND CONVERSION FACTORS Proton mass, m p Neutron mass, mn Electron mass, me Avogadro's number, N 0 Universal gas constant, 1.67
1.67 10
10 27
27 31 kg
kg kg Electron charge magnitude, e 1.60 10 19 C 1 electron volt, 1 eV Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth's surface, 1.60 10 19 J 9.11 10 6.02 c G 3.00 6.67 108 m s 10
11 1023 mol 1 m 3 kg s2 R 8.31 J (mol K) 1.38 10
23 g 9.8 m s2 Boltzmann's constant, k B J K 1u
h hc 1 unified atomic mass unit, Planck's constant, Vacuum permittivity, Coulomb's law constant, k Vacuum permeability, Magnetic constant, k 1 atmosphere pressure, meter, kilogram, second, ampere, kelvin, m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J 1.66
6.63 1.99 8.85 9.0 4p 10
7 10
10 10 10 27
34 25 12 kg
Js Jm
2 931 MeV c 2
4.14 1.24
2 10 15 3 eV s 10 eV nm 0 C Nm 1 4p 0 109 N m 2 C2 10
7 m0 m0 4 p (T m) A (T m) A 1 atm 1.0 105 N m 2
W C V W H 1.0 105 Pa
F T C eV UNIT SYMBOLS watt, coulomb, volt, ohm, henry, farad, tesla, degree Celsius, electronvolt, PREFIXES Factor Prefix Symbol
10 9 106 103 10
2 VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q 30 0 37 45 53 60 90 giga mega kilo centi milli micro
nano pico G M k c m sin q
cos q tan q 0 1 0 12
3 2 3 3 35 45 34 2 2 2 2
1 45 35 43 3 2 1 0 12
3 10 3 10 6
10
9 m
n p 10 12 The following conventions are used in this exam. 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 2008 and 2009 MECHANICS ELECTRICITY AND MAGNETISM u u0 at x x0 u0 t 1 2 at 2 u2 u0 2 2a x ma x0 F
F
J Fnet
dp dt
F dt a F f h I J K k Dp p
Ffric W K P P DUg mv
mN
F dr
1 mu 2 2 dW dt F v
mgh = = = = = = = = = L = m= N = P = p = r = r = T = t = U= u = W= x = m= q = t = w= a= acceleration force frequency height rotational inertia impulse kinetic energy spring constant length angular momentum mass normal force power momentum radius or distance position vector period time potential energy velocity or speed work done on a system position coefficient of friction angle torque angular speed angular acceleration F
E 1 q1q2 4p 0 r 2
F q E dA Q
0 A B C d E E V dV dr 1 4p 0 qi ri = = = = = e= F = I = J = L = = n = i N = UE
C C Cp 1 Cs I qV
Q V k
0A 1 4p 0 q1q2 r d
i Ci 1 i Ci dQ dt 1 QV 2 1 CV 2 2 P = Q= q = R = r = t = U= V= u = r= area magnetic field capacitance distance electric field emf force current current density inductance length number of loops of wire per unit length number of charge carriers per unit volume power charge point charge resistance distance time potential or stored energy electric potential velocity or speed resistivity fm = magnetic flux k = dielectric constant ac u2 r w2r Fs kx
1 2 kx 2 t
t Uc B d m0 I r F
t net Ia mr 2 Us T R
1 f E I I r 2 dm 2p w r A
rJ Neud A dB
F Bs
fm m0 I d r 4p r3
Id
m0 nI B rcm
u rw mr m Ts
Tp
FG 2p
2p m k
g ^ r V
Rs IR
i B dA L
K w q r p Iw Ri e
e
B
UL 1 2 Iw 2 Gm1m2 r2 1 Rp P IV i 1 Ri d fm dt
L dI dt w0 q0 at UG
w0 t
1 2 at 2 Gm1m2 r FM qv 1 2 LI 2 3 ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2008 and 2009 GEOMETRY AND TRIGONOMETRY
Rectangle A bh Triangle CALCULUS A
Circle 1 bh 2 pr 2 A C 2pr Parallelepiped V wh Cylinder
V
pr 2 A= C= V= S = b = h = = w= r = area circumference volume surface area base height length width radius df dx
d n x dx d x e dx d f du du dx
nx n ex 1 x cos x sin x 1 n
ex
1 d 1n x dx d sin x dx d cos x dx x n dx S
Sphere 2pr
4 3 pr 3 4pr 2 2pr 2 1 x n 1, n 1 e x dx dx x V S a2
sin q cos q tan q ln x
sin x cos x cos x dx Right Triangle b2 a c b c a b c2
c q b 90 a sin x dx 4 2008 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE 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 the pink booklet in the spaces provided after each part, NOT in this green insert. E&M. 1. A metal sphere of radius a contains a charge +Q and is surrounded by an uncharged, concentric, metallic shell of inner radius b and outer radius c, as shown above. Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Determine the induced charge on each of the following and explain your reasoning in each case. i. The inner surface of the metallic shell ii. The outer surface of the metallic shell (b) Determine expressions for the magnitude of the electric field E as a function of r, the distance from the center of the inner sphere, in each of the following regions. i. r ii. a a r r
r b c iii. b iv. c 2008 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. 5 2008 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS
(c) On the axes below, sketch a graph of E as a function of r. (d) An electron of mass me carrying a charge e is released from rest at a very large distance from the spheres. Derive an expression for the speed of the particle at a distance 10r from the center of the spheres. 2008 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. 6 2008 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS E&M. 2. In the circuit shown above, A and B are terminals to which different circuit components can be connected. (a) Calculate the potential difference across R2 immediately after the switch S is closed in each of the following cases. i. A 50 resistor connects A and B. ii. A 40 mH inductor connects A and B. iii. An initially uncharged 0.80 F capacitor connects A and B. (b) The switch gets closed at time t 0 . On the axes below, sketch the graphs of the current in the 100 W resistor R3 versus time t for the three cases. Label the graphs R for the resistor, L for the inductor, and C for the capacitor. 2008 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. 7 2008 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREERESPONSE QUESTIONS Figure 1 E&M. 3. The circular loop of wire in Figure 1 above has a radius of R and carries a current I. Point P is a distance of R 2 above the center of the loop. Express algebraic answers to parts (a) and (b) in terms of R, I, and fundamental constants. (a) i. State the direction of the magnetic field B1 at point P due to the current in the loop. ii. Calculate the magnitude of the magnetic field B1 at point P. Figure 2 Figure 3 A second identical loop also carrying a current I is added at a distance of R above the first loop, as shown in Figure 2 above. (b) Determine the magnitude of the net magnetic field Bnet at point P. A small square loop of wire in which each side has a length s is now placed at point P with its plane parallel to the plane of each loop, as shown in Figure 3 above. For parts (c) and (d), assume that the magnetic field between the two circular loops is uniform in the region of the square loop and has magnitude Bnet . (c) In terms of Bnet and s, determine the magnetic flux through the square loop. (d) The square loop is now rotated about an axis in its plane at an angular speed . In terms of Bnet , s, and , calculate the induced emf in the loop as a function of time t, assuming that the loop is horizontal at t 0 . END OF EXAM 2008 The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). 8 ...
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