AP Physics C Electricity and Magnetism 2019 Free Response Questions Set 2 2019 AP ® Physics C Electricity and Magnetism Free Response Questions Set 2 © 2019 The College Board College Board, Advanced P[.]
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Physics C:
Electricity and
Magnetism
Free-Response Questions
Set 2
Trang 2
ADVANCED PLACEMENT PHYSICS C TABLE OF INFORMATION
-2-CONSTANTS AND CONVERSION FACTORS Proton mass, m p 1.671027 kg
Neutron mass, m n 1.671027 kg
Electron mass, m e 9.111031 kg
Avogadro’s number, N0 6.0210 mol23 1
Universal gas constant, R 8.31 J (mol K)<
Boltzmann’s constant, k B 1.381023J K
Electron charge magnitude, e 1.601019 C
1 electron volt, 1 eV 1.601019 J Speed of light, c 3.0010 m s8 Universal gravitational
6.67 10 N m kg
G <
Acceleration due to gravity
at Earth’s surface,
2 9.8 m s
g
1 unified atomic mass unit, 1 u 1.661027 kg 931 MeV c2
Planck’s constant, h 6.631034 J s< 4.141015 eV s<
1.99 10 J m 1.24 10 eV nm
Vacuum permittivity, e0 8.851012 C2 N m< 2 Coulomb’s law constant, 9 2 2
0
1 4 9.0 10 N m C
Vacuum permeability, m0 4p 107 (T m) A<
Magnetic constant, 7
0 4 1 10 (T m) A
k m p <
1 atmosphere pressure, 1 atm 1.010 N m5 2 1.010 Pa5
UNIT
SYMBOLS
meter, m kilogram, kg second, s ampere, A kelvin, K
mole, mol hertz, Hz newton, N pascal, Pa joule, J
watt, W coulomb, C volt, V
henry, H
tesla, T degree Celsius, C electron volt, eV
PREFIXES
Factor Prefix Symbol
9
10 giga G
6
10 mega M
3
10 kilo k
2
3
6
9
10 nano n
12
10 pico p
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
q 0D 30D 37D 45D 53D 60D 90D
The following assumptions are used in this exam
I The frame of reference of any problem is inertial unless otherwise stated
II The direction of current is the direction in which positive charges would drift
III The electric potential is zero at an infinite distance from an isolated point charge
IV All batteries and meters are ideal unless otherwise stated
V Edge effects for the electric field of a parallel plate capacitor are negligible unless otherwise stated
Trang 3ADVANCED PLACEMENT PHYSICS C EQUATIONS MECHANICS
a = acceleration
E = energy
F = force
f = frequency
h = height
I = rotational inertia
J = impulse
K = kinetic energy
k = spring constant
A = length
L = angular momentum
m = mass
P = power
p = momentum
r = radius or distance
T = period
t = time
U = potential energy
v = velocity or speed
W = work done on a system
x = position
m = coefficient of friction
q = angle
t = torque
w = angular speed
a = angular acceleration
f = phase angle
0
à x à x a t x
2
0 0
1 2
Ã
x x
2
2
à x à x a x x x0
net
F
F
a
G
G
G dp
F
dt
D
JG F dtG p
pG mvG
m
D E W ÔF d rG< G
2
1
2 Ã
dE
P
dt
G G
<
P F v
DU g mg hD
2
2
c
a
t G Gr F G
t
t
a Ç
G
G
2
I Ôr dm Çm r2
i i
cm
i
m x
x
m
Ç
Ç
à r w
w
L r p I
2
1
2
K I w
0 t
w w a
D G
G
s
2
1
2 D
s
maxcos(
T
f
p w
2
T
k p
2
p T
g
p A
1 2 2
G
G
Gm m F
r
1 2
G
Gm m U
r
ELECTRICITY AND MAGNETISM
A = area
B = magnetic field
C = capacitance
d = distance
E = electric field
e = emf
F = force
I = current
J = current density
L = inductance
A = length
n = number of loops of wire per unit length
N = number of charge carriers per unit volume
P = power
Q = charge
q = point charge
R = resistance
r = radius or distance
t = time
U = potential or stored energy
V = electric potential
v = velocity or speed
r = resistivity
F = flux
k = dielectric constant
2
1 2 0
1
4pe
G
E
q q F
r
G F E E q
G
0
e
Ô G< G
vE dA Q
E
dx
DV ÔE drG G<
0
1
4pe Ç i
i i
q V
r
1 2 0
1
4pe
E
q q
U qV
r
DV Q C
0
k e A C
d
i
C ÇC
C ÇC dQ I dt
2
C
U Q VD C DV R
A
rA
r
d
I Nev A
DV I R
s
R ÇR
i i p
R ÇR
G
G
M
F qv B
0
m
Ô G< AG
0 2 4
m p
G
G I dA r dB
r
G
A
0
s
B m nI
F B ÔB dAG< G
e v ÔE dG< AG dFB
dt dI
L dt
e
2 1 2
L
Trang 4-4-ADVANCED PLACEMENT PHYSICS C EQUATIONS
GEOMETRY AND TRIGONOMETRY
A = area
C = circumference
V = volume
S = surface area
b = base
h = height
= length
w = width
r = radius
s = arc length
q = angle
Rectangle
A bh
Triangle
1
2
A bh
Circle
2
A r p
2
C p r
s rq
Rectangular Solid
V h w
Cylinder
2
V p r
2
S p r p r
Sphere
3
4
3
V p r
2
4
S p r
Right Triangle
a b c
sin a
c
q
cos b
c
q
tan a
b
q
s
r q
b
90°
q
CALCULUS
d f d f du
dx du dx
d x nx dx
n
ax ax
d e ae dx
d ax
1
ln
>sin @ cos
d
dx
>cos @ sin
dx
1 1
1
n n
n
1
Ôe dx ax e ax
a
ln
x a
a
sin cos
a
VECTOR PRODUCTS
cos
A B AB q
sin
A B AB q
Trang 52019 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
1 The circuit represented above is composed of three resistors with the resistances shown, a battery of voltage V ,0
a capacitor of capacitance C, and a switch S The switch is closed, and after a long time, the circuit reaches
steady-state conditions Answer the following questions in terms of V , R, C, and fundamental constants, as0
appropriate
(a) Derive an expression for the steady-state current supplied by the battery
(b) Derive an expression for the charge on the capacitor
(c) Derive an expression for the energy stored in the capacitor
Now the switch is opened at time t = 0.
(d) Write, but do NOT solve, a differential equation that could be used to solve for the charge q t on the( )
capacitor as a function of the time t after the switch is opened.
Trang 62019 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS
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-6-(e)
i Calculate the current in resistor R immediately after the switch is opened
ii On the axes below, sketch the current in the circuit as a function of time from time t = 0 to a long time
after the switch is opened Explicitly label the maxima with numerical values or algebraic expressions,
as appropriate
(f) Is the total amount of energy dissipated in the resistors after the switch is opened greater than, less than, or equal to the amount of energy stored in the capacitor calculated in part (c) ?
Greater than Less than Equal to
Justify your answer
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Trang 72019 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS
2 A nonconducting hollow sphere of inner radius 0.030 m and outer radius 0.050 m carries a positive volume
charge density r , as shown in the figure above The charge density r of the sphere is given as a function of the distance r from the center of the sphere, in meters, by the following
r < 0.030 m: r = 0
b = ¥ -6 2
0.030 m < r < 0.050 m: r = b r, where 1.6 10 C m
r > 0.050 m: r = 0 (a) Calculate the total charge of the sphere
(b) Using Gauss’s law, calculate the magnitude of the electric field E at the outer surface of the sphere
(c) On the axes below, sketch the magnitude of the electric field E as a function of distance r from the center
of the sphere
Trang 82019 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS
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-8-(d) Calculate the electric potential V at the outer surface of the sphere Assume the electric potential to be zero
at infinity
(e) A proton is released from rest at the outer surface of the sphere at time t = 0 s.
i Calculate the magnitude of the initial acceleration of the proton
ii Calculate the speed of the proton after a long time
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Trang 92019 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS
3 Two plates are set up with a potential difference V between them A small sphere of mass m and charge –e
is placed at the left-hand plate, which has a negative charge, and is allowed to accelerate across the space
between the plates and pass through a small opening After passing through the small opening, the sphere
enters a region in which there is a uniform magnetic field of magnitude B directed into the page, as shown
above Ignore gravitational effects Express all algebraic answers in terms of V, m, e, B, and fundamental
constants, as appropriate
(a)
i What is the initial direction of the force on the sphere as it enters the magnetic field?
Out of the page Toward the top of the page Toward the bottom of the page
ii Describe the path taken by the sphere after it enters the magnetic field
(b) Derive an expression for the speed of the sphere as it passes through the small opening
(c) Derive an expression for the radius of the path taken by the sphere as it moves through the magnetic field
Trang 102019 AP® PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS
-10-An experiment is performed in which a beam of electrons is accelerated across the space between the plates and passes through the small opening After passing through the opening, the electrons travel in a semicircular path and strike the right-hand plate The potential difference between the plates is varied in regular increments, as shown in the table below For each potential difference, the magnetic field is varied in order to cause the beam to strike the right-hand plate at a distance of 0.020 m from the opening
(d) Indicate below which quantities should be graphed to yield a straight line whose slope could be used to
calculate a numerical value for the mass-to-charge ratio of an electron
Vertical axis:
Horizontal axis:
Use the remaining columns in the table above, as needed, to record any quantities that you indicated that are not given Label each column you use and include units
(e) On the graph below, plot the relationship determined in part (d) Clearly scale and label all axes, including units, if appropriate Draw a straight line that best represents the data
(f) Using the straight line from part (e), determine the mass-to-charge ratio of an electron
STOP END OF EXAM
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... data-page="5">20 19 AP< /b>® PHYSICS C: ELECTRICITY AND MAGNETISM FREE- RESPONSE QUESTIONS
PHYSICS C: ELECTRICITY AND MAGNETISM< /b>... data-page="7">
20 19 AP< /b>® PHYSICS C: ELECTRICITY AND MAGNETISM FREE- RESPONSE QUESTIONS
A nonconducting hollow sphere of inner radius 0.030 m and outer... data-page="9">
20 19 AP< /b>® PHYSICS C: ELECTRICITY AND MAGNETISM FREE- RESPONSE QUESTIONS
3 Two plates are set up with a potential