Download 2002 AP Physics C: Electricity and Magnetism Free

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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,
Universal gas constant,
N0 = 6.02 × 10 mol
23
−1
R = 8.31 J / ( mol ¼ K )
mole
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
hc = 1.99 × 10 −25 J ⋅ m
= 1.24 × 10 3 eV ⋅ nm
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 = 8.85 × 10
−12
C / N⋅m
2
2
k = 1 / 4π ⑀ 0 = 9.0 × 10 N ⋅ m 2 / C 2
9
µ 0 = 4π × 10 −7 (T ⋅ m ) / A
k = µ 0 / 4π = 10 (T ⋅ m ) / A
−7
G
= 6.67 ™ 10 -11 m 3 / kg ¼ s 2
g = 9.8 m / s
2
1 atm = 1.0 × 10 5 N / m 2
= 1.0 × 10 Pa
10
−6
VALUES OF TRIGONOMETRIC FUNCTIONS
FOR COMMON ANGLES
joule
J
watt
W
θ
coulomb
C
0
volt
V
ohm
Ω
henry
H
farad
F
tesla
T
45o
o
sin θ
cos θ
tan θ
0
1
0
3 /2
3 /3
30o
1/2
37o
3/5
degree
Celsius
o
C
53o
electronvolt
eV
60o
90o
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 = Fⴢv
U = potential energy
u = velocity or speed
DUg = mgh
W
= work done on a system
2
u
2
x
= position
ac =
= w r
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
1 q1 q 2
A = area
F=
2
B = magnetic field
4 p⑀ 0 r
C = capacitance
F
d = distance
E=
q
E = electric field
e = emf
Q
养 E • dA =
F = force
⑀0
I = current
dV
L = inductance
E=−
l = length
dr
n
= number of loops of wire per
q
1
i
V=
unit length
4 p⑀ 0 i ri
P = power
∑
UE = qV =
1 q1 q 2
4 p⑀ 0 r
Q
V
k⑀ A
C= 0
d
C p = ∑ Ci
C=
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
养 B • d ø = m0 I
I
F = I dø × B
Bs = m0 nI
I
fm = B • dA
dfm
dt
dI
e = −L
dt
1 2
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 =
b
c
tan q =
a
b
A=
C=
V=
S =
b =
h =
l=
w=
r =
area
circumference
volume
surface area
base
height
length
width
radius
c
q
a
90
b
CALCULUS
df
d f du
=
dx
du dx
2 7
2 7
d n
n -1
x = nx
dx
d x
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.
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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.
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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.
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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