Practice Workbook Electricity and Magnetism PDF

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AP Physics C – Practice Workbook – Book 2 Electricity and Magnetism

…. The following(© is applicable to this entire document – copies for student distribution for exam preparation explicitly allowed. 1) Copyright © 1973-2012 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners.

2012-2013

Table of Contents Table of Information and Equation Tables ......................................................................................3

Chapter 8 Electrostatics Electrostatics Multiple Choice ........................................................................................................... Section A – Coulomb’s Law and Coulomb’s Law Methods .............................................11 Section B – Gauss’s Law ...................................................................................................16 Section C – Electric Potential And Energy ........................................................................19 Section D – Capacitance ....................................................................................................31 Electrostatics Free Response.............................................................................................................. Section A – Coulomb’s Law and Coulomb’s Law Methods .............................................35 Section B – Gauss’s Law ...................................................................................................41 Section C – Electric Potential And Energy ........................................................................54 Section D – Capacitance ....................................................................................................62 Answers to Electrostatics Questions ..............................................................................................67

Chapter 9 Circuits Circuits Multiple Choice ................................................................................................................91 Circuits Free Response ..................................................................................................................99 Answers to Circuits Questions .....................................................................................................113

Chapter 10 Magnetism and Induction Magnetism and Induction Multiple Choice Section A – Magnetostatics .............................................................................................125 Section B – Biot Savart and Ampere’s Law ....................................................................130 Section C – Induction and Inductance .............................................................................134 Magnetism and Induction Free Response Section A – Magnetostatics .............................................................................................141 Section B – Biot Savart and Ampere’s Law ....................................................................147 Section C – Induction and Inductance .............................................................................155 Answers to Magnetism and Induction Questions ........................................................................187

This book is a compilation of all the problems published by College Board in AP Physics C organized by topic. The problems vary in level of difficulty and type and this book represents an invaluable resource for practice and review and should be used… often. Whether you are struggling or confident in a topic, you should be doing these problems as a reinforcement of ideas and concepts on a scale that could never be covered in the class time allotted. The answers as presented are not the only method to solving many of these problems and physics teachers may present slightly different methods and/or different symbols and variables in each topic, but the underlying physics concepts are the same and we ask you read the solutions with an open mind and use these differences to expand your problem solving skills. Finally, we are fallible and if you find any typographical errors, formatting errors or anything that strikes you as unclear or unreadable, please let us know so we can make the necessary announcements and corrections.

Table of Information and Equation Tables for AP Physics Exams The accompanying Table of Information and Equation Tables will be provided to students when they take the AP Physics Exams. Therefore, students may NOT bring their own copies of these tables to the exam room, although they may use them throughout the year in their classes in order to become familiar with their content. Check the Physics course home pages on AP Central for the latest versions of these tables (apcentral.collegeboard.com). Table of Information For both the Physics B and Physics C Exams, the Table of Information is printed near the front cover of the multiple-choice section and on the green insert provided with the free-response section. The tables are identical for both exams except for one convention as noted. Equation Tables For both the Physics B and Physics C Exams, the equation tables for each exam are printed only on the green insert provided with the free-response section. The equation tables may be used by students when taking the free-response sections of both exams but NOT when taking the multiple-choice sections. The equations in the tables express the relationships that are encountered most frequently in AP Physics courses and exams. However, the tables do not include all equations that might possibly be used. For example, they do not include many equations that can be derived by combining other equations in the tables. Nor do they include equations that are simply special cases of any that are in the tables. Students are responsible for understanding the physical principles that underlie each equation and for knowing the conditions for which each equation is applicable. The equation tables are grouped in sections according to the major content category in which they appear. Within each section, the symbols used for the variables in that section are defined. However, in some cases the same symbol is used to represent different quantities in different tables. It should be noted that there is no uniform convention among textbooks for the symbols used in writing equations. The equation tables follow many common conventions, but in some cases consistency was sacrificed for the sake of clarity. Some explanations about notation used in the equation tables: 1. The symbols used for physical constants are the same as those in the Table of Information and are defined in the Table of Information rather than in the right-hand columns of the tables. 2. Symbols in bold face represent vector quantities. 3. Subscripts on symbols in the equations are used to represent special cases of the variables defined in the right-hand columns. 4. The symbol D before a variable in an equation specifically indicates a change in the variable (i.e., final value minus initial value). 5. Several different symbols (e.g., d, r, s, h, � ) are used for linear dimensions such as length. The particular symbol used in an equation is one that is commonly used for that equation in textbooks.

3 © 2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

TABLE OF INFORMATION DEVELOPED FOR 2012 (see note on cover page) CONSTANTS AND CONVERSION FACTORS Proton mass, m p = 1.67 ¥ 10-27 kg

e = 1.60 ¥ 10- 19 C

Electron charge magnitude,

Neutron mass, mn = 1.67 ¥ 10 -27 kg

1 electron volt, 1 eV = 1.60 ¥ 10 -19 J

Electron mass, me = 9.11 ¥ 10 -31 kg

Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface,

Avogadro’s number, N 0 = 6.02 ¥ 10 23 mol -1

R = 8.31 J (moliK)

Universal gas constant,

c = 3.00 ¥ 108 m s G = 6.67 ¥ 10-11 m3 kg is2 g = 9.8 m s2

Boltzmann’s constant, kB = 1.38 ¥ 10 -23 J K 1 u = 1.66 ¥ 10 27 kg = 931 MeV c 2

1 unified atomic mass unit,

h = 6.63 ¥ 10- 34 J is = 4.14 ¥ 10- 15 eV is

Planck’s constant,

hc = 1.99 ¥ 10- 25 J im = 1.24 ¥ 10 3 eV inm 0 = 8.85 ¥ 10 - 12 C2 Ni m 2

Vacuum permittivity,

Coulomb’s law constant, k = 1 4 p 0 = 9.0 ¥ 109 N im 2 C 2 m0 = 4 p ¥ 10 - (Ti m) A 7

Vacuum permeability,

Magnetic constant, k ¢ = m0 4 p = 1 ¥ 10 - 7 (T im) A

1 atm = 1.0 ¥ 105 N m2 = 1.0 ¥ 105 Pa

1 atmosphere pressure,

UNIT SYMBOLS

meter, kilogram, second, ampere, kelvin,

PREFIXES Factor Prefix Symbol

m kg s A K

mole, hertz, newton, pascal, joule,

mol Hz N Pa J

watt, coulomb, volt, ohm, henry,

W C V W H

farad, tesla, degree Celsius, electron-volt,

F T ∞C eV

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q

0�

30�

45�

53�

60�

90�

2 2

4 5

3 2

1

10 9

giga

G

sin q

0

12

37� 35

10 6

mega

M

cosq

1

3 2

4 5

2 2

35

12

0

3

kilo

k

tan q

0

3 3

34

1

43

3

•

-2

centi

c

-3

milli

m

10- 6

micro

m

10 - 9

nano

n

10-12

pico

p

10 10 10

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. *IV. For mechanics and thermodynamics equations, W represents the work done on a system. *Not on the Table of Information for Physics C, since Thermodynamics is not a Physics C topic.

4 © 2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

ADVANCED PLACEMENT PHYSICS B EQUATIONS DEVELOPED FOR 2012 NEWTONIAN MECHANICS

u = u0 + at

x = x0 + u 0 t +

1 2 at 2

u2 = u0 2 + 2a ( x - x0 )

 F = Fnet = m a F fric £ m N 2

u ac = r

t = r F sin q

p = mv J = FDt = Dp 1 K = mu 2 2 DU g = mgh W = F Dr cos q Pavg =

W Dt

a = F = f = h = J = K = k = � = m= N = P = p = r = T = t = U= u = W= x m q t

= = = =

acceleration force frequency height impulse kinetic energy spring constant length mass normal force power momentum radius or distance period time potential energy velocity or speed work done on a system position coefficient of friction angle torque

ELECTRICITY AND MAGNETISM

d

= = = = = e= F = I = � = P = Q = q = R = r = t = U=

1 1 QV = CV 2 2 2

V=

F =

kq1q2 r2

E =

F q

UE = qV = Eavg = -

kq1 q2 r

V d

q q Êq ˆ V = k Á 1 + 2 + 3 + ...˜ r2 r3 Ë r1 ¯ C =

Q V

C =

 0A

Uc =

I avg = R =

DQ Dt

r� A

V = IR C p = C 1 + C 2 + C 3 + ...

Fs = -k x

1 1 1 1 = + + + ... C s C1 C2 C3

1 2 kx 2

R s = R1 + R2 + R3 + ...

1 1 1 1 = + + + ... Rp R1 R 2 R3

m Ts = 2 p k

FB = qu B sin q

� Tp = 2 p g T =

FB = BI � sin q

1 f

FG = -

B =

Gm1m2

UG = -

u = r = q = fm =

area magnetic field capacitance distance electric field emf force current length power charge point charge resistance distance time potential (stored) energy electric potential or potential difference velocity or speed resistivity angle magnetic flux

P = IV

P = Fu cos q

Us =

A B C d E

r

2

Gm1m 2 r

m0 I 2p r

fm = BAcos q

eavg

e

=-

Dfm Dt

= B �u

5 © 2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

ADVANCED PLACEMENT PHYSICS B EQUATIONS DEVELOPED FOR 2012 FLUID MECHANICS AND THERMAL PHYSICS

WAVES AND OPTICS

r= mV

u = fl

P = P0 + r gh

Fbuoy = rVg

A1u1 = A2 u2 P + r gy +

1 2 ru = const. 2

D � = a � 0 DT

H =

kAD T L

P=

F A

PV = nRT = NkB T K avg =

3 k T 2 B

urms =

3 RT = M

W = -PD V DU = Q + W

W e= QH ec =

3 kB T m

A = area e = efficiency F = force h = depth H = rate of heat transfer k = thermal conductivity K avg = average molecular kinetic energy � = length L = thickness m = mass M = molar mass n = number of moles N = number of molecules P = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u = velocity or speed u rms = root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion m = mass of molecule r = density

TH - T C TH

K max = hf - f

l =

h p

DE = ( Dm) c 2

c u

n1 sin q1 = n2 sin q 2 sin q c =

n2 n1

1 1 1 + = si s0 f h s M = i =- i h0 s0

f = R 2 d sin q = m l

xm ª

ml L d

GEOMETRY AND TRIGONOMETRY

Rectangle A = bh Triangle 1 A = bh 2 Circle A = pr 2 C = 2p r Rectangular Solid V = �wh Cylinder V = p r 2�

A = area C = circumference V = volume S = surface area b = base h = height � = length w = width r = radius

S = 2 p r� + 2 p r 2 Sphere 4 V = p r3 3

ATOMIC AND NUCLEAR PHYSICS

E = hf = pc

n =

d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q = angle

E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function

S = 4p r 2

Right Triangle a2 + b2 = c 2 a sin q = c b cosq = c a tan q = b

c

6 © 2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

a 90°

q b

ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR 2012 MECHANICS u = u0 + at

x = x0 + u0 t +

1 2 at 2

u 2 = u0 2 + 2a ( x - x0 )

 F = Fnet = m a F=

dp dt

J=

Ú Fdt = D p

p = mv Ffric £ m N W =

Ú Fidr

K =

1 2 mu 2

P=

dW dt

P = F iv DUg = mgh ac =

2

u = w2 r r

a = F = f = h = I = J = K = k = � = L = m= N = P = p = r = r = T = t = U= u = W= x = m = q = t = w = a = f =

ELECTRICITY AND MAGNETISM

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 phase angle

1 q1 q2 4p 0 r 2

F=

E= F q

�Ú E i dA =

0

q

1 4 p 0

 rii

UE = qV = C =

Q V

C =

k 0 A d i

1 1 =Â Cs C i i

I =

dQ dt

�Ú B i d  = m0I

R =

r� A

dB =

Us =

I = Ú r 2 dm = Â mr 2

x = xmax cos( wt + f)

E = rJ

rcm =  mr  m

2p 1 T = = w f

I = Neud A

m k

Ts = 2 p

1 K = I w2 2

Tp = 2 p

w = w0 + a t

Gm1 m2 ˆ FG = r 2 r

q = q0 + w0 t +

1 2 at 2

UG

� g

Gm1m2 =r

= = = = = = = V= u = r = fm = k =

P Q q R r t U

1 1 QV = CV 2 2 2

 t = t net = I a

L = r ¥ p = Iw

N =

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 potentia l velocity or speed resistivity magnetic flux dielectric constant

Uc =

t= r¥F

u = rw

1 q1 q2 4 p 0 r

 Ci

Cp =

F I J L � n

= = = = = = = = = = = =

i

Fs = -k x

1 2 kx 2

e

Q

dV E=dr V =

A B C d E

 Ri

1 = Rp

Ú

F = I d ¥ B

V = IR Rs =

m0 I d ¥ r 4p r 3

B s = m0 nI fm =

Ú B i dA

e

=

�Ú E i d  = -

e

= -L

i

 i

1 Ri

P = IV FM = q v ¥ B

UL =

d fm dt

dI dt

1 2 LI 2 7

© 2011 The College Board. Visit the College Board on the Web: www.collegeboard.org.

ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR 2012 GEOMETRY AND TRIGONOMETRY Rectangle

A = bh Triangle A =

1 bh 2

Circle

A = pr 2

C = 2 pr Rectangular Solid

CALCULUS

A = area C = circumference V = volume S = surface area b = base h = height � = length w = width r = radius

df d f du = dx du dx

d n (x ) = nxn - 1 dx d x ( e ) = ex dx d (ln x ) = 1 dx x d (sin x ) = cosx dx

V = � wh Cylinder

d (cos x ) = - sin x dx

V = pr2 �

Ú xn dx =

S = 2pr � + 2 p r 2

Ú ex dx = e

x

Sphere

V =

4 3 pr 3

Ú

dx = ln x x

Ú cosx dx = sin x

S = 4 pr 2

Ú sinx dx = - cosx

Right Triangle 2

1 xn+ 1 n , π 1 n+ 1

2

a + b = c2 sin q =

a c

b cos q = c tan q =

c

a 90°

q b

a b

8 © 2011 The Co...