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Sample Common Exam 3, Example # 2
(Spring 2013
Phys 121H)
1. For the RC circuit shown ( R = 2MΩ, C = 3 µF and Ε = 300 V) how long will take for the current to
reach value of 77 µA after the switch is closed?
A. 1 s
B. 2 s
C. 3 s
D. 4 s
E. 5 s
2. Suppose the switch has been closed for a time interval sufficiently long for the capacitor to become fully
charged. Find the charge on the capacitor.
A) 0.045C
B) 0. 75 mC
C) 12 x10-6C
D) 2 .0 C
E) 50 µC
3. 0 Consider the circuit below:
90 Ω
100 V
30 Ω
60 V
150 Ω
What is the current through resistor 30 Ω in the circuit at right?
a. 2.5 A
b. 0.33 A
c. 4.7 A
d. 0.63 A
e. 0.08 A
4.
a.
b.
c.
d.
e.
What is the current through 60 V battery?
0.77 A
0 44 A
0.11 A
1.24 A
0.55 A
5. An electron moving in the positive x direction experiences a magnetic force in the positive z direction. If Bx = 0, what is the direction of
the magnetic field?
a. negative y direction
b. positive y direction
c. negative z direction
d. positive z direction
e. negative x direction
1
6. A particle (mass = 6.0 mg) moves with a speed of 4.0 km/s in a direction that makes an angle of 37° above the positive x axis in the xy
plane. At the instant it enters a magnetic field of (5.0 ) mT it experiences an acceleration of (8.0 ) m/s2. What is the charge of the
particle?
a.
b.
c.
d.
e.
−4.8 µC
8.0 µC
−4.0 µC
4.8 µC
−5.0 µC
7. What is the magnitude of the magnetic force on a charged particle (Q = 5.0 µC) moving with a speed of 80 km/s in the positive x
direction at a point where Bx = 5.0 T, By = −4.0 T, and Bz = 0.0 T?
a.
b.
c.
d.
e.
2.8 N
1.6 N
1.2 N
2.0 N
0.4 N
8. An electron follows a circular path (radius = 15 cm) in a uniform magnetic field (magnitude = 0.3 mT). What is the period
of this motion?
a.
b.
c.
d.
e.
0.12 µs
1.2 ms
0.18 µs
1.8 ms
1.8 µs
9. An electron moving with a speed of 2x105 m/s enters a region between two parallel plates separated by d = 20 mm with a potential
difference of V = 100 V between them. The electron is moving perpendicular to the electric field of the plates when it enters the region
between the plates. What uniform magnetic field , perpendicular to both the electron path and the electric field, must be applied for the
electron not be deflected?
A.
B.
C.
D.
E.
10 mT
15 mT
20 mT
25 mT
30 mT
10. What is the kinetic energy of an electron that passes undeflected through perpendicular electric and magnetic fields if E = 4.0 kV/m
and B = 8.0 mT?
a.
b.
c.
d.
e.
8.65 eV
0.71 eV
2.84 eV
0.054 eV
1.4 eV
11.
A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given
by B = (30 − 40 ) mT. What is the resulting magnetic force on the wire?
a.
b.
c.
d.
e.
(+1.2
(−
−1.2
(−1.5
(+1.5
(+0.90
)N
)N
)N
)N
)N
2
12 – 13. Two long, straight wires are parallel and carry the same current of i1 = i2 = 6 A in the opposite direction as shown.
12. If the distance between the wires is 6 cm, and the distance from wire 1 to point B is 2 cm what are the direction
and the magnitude of the net magnetic field at point B seen in figure.
A. 3.5x10-5 T into the page
B. 4.5x10-5 T into the page
C. 1.6x10-4 T out of the page
D. 2.0x10 -4T into the page
E. 8.0x10-3 T out of the page
13. What are the direction and the magnitude of the force per unit length F/L that the wire 1 exerts on the wire 2?
A. 1.2 x10-4 N, to the left
B. 1.2 x10-4 N, to the right
C. 5.0 x10-3 N, up
D. 5.0x10-3 N, down
E. 0.8x10-3 N, to the page
14. An electron with charge 1.6.10-19C and mass 9.11x10-31 kg is moving with a velocity v=2.105 m/s in the negative z
direction. A magnetic field B = 0.125 mT is pointing in the negative x direction . Find the frequency of electron
circular motion.
A)
B)
C)
D)
E)
1.9 MHz
2.2 MHz
3.5 MHz
4.2 MHz
5.1 MHz
15. A current loop is oriented in three different positions relative to a uniform magnetic field. In position 1 the plane of the loop is
perpendicular to the field lines. In position 2 and 3 the plane of the loop is parallel to the field as shown. The torque on the loop is
maximum in
a.
Only position 1.
b.
Only position 2.
c.
Only position 3
d.
positions 2 and 3.
(1)
(2)
(3)
e.
all three positions
16. What is the magnitude of the magnetic field inside a solenoid that is 10-cm long with 1000 turns of wire carrying a current of 0.1 A?
A)
B)
C)
D)
E)
1.26×10–5 T
1.26×10–4 T
1.26×10–3 T
100 T
1000 T
17. A particle with positive charge q = 5x10-6 C is a distance 1.5 cm from a long straight wire that carries a
current 5 A. The particle is traveling with speed 12000 m/s perpendicular to the wire as shown in the figure.
What are the direction and magnitude of the force on the particle if it is moving away from the wire?
A) 1.0x10-7 N, up
B) 1.0x10-7 N, down
C) 2.0x10-8 N, up
D) 4.0x10-6 N, down
E) 4.0x10-6 N, up
3
18.
What is the magnitude of the magnetic field at point P if a = R and b = 2R?
a.
b.
c.
d.
e.
19. If a = 5.0 cm, b = 8.0 cm, and I = 30 A, what is the magnitude of the magnetic field at point P?
a.
82 µT
b.
5.9 µT
c.
35 µT
d.
18 µT
e.
0. 8 µT
20. Two long wires are oriented so that they are perpendicular to each other, and at their closest, they are 20 cm apart. What is the
magnitude of the magnetic field at a point midway between them if the top one carries a current of 20-A and the bottom one caries 10-A?
A) 4.5x10-5 T
B) 2.0x10-5 T
C) 4.0x10-7 T
D) 1.0x10-2 T
E) 4.0x10-4 T
21. The current in the loop is 2 A counterclockwise , the radius of the larger semi-loop is 25 cm and radius of the smaller semi-loop is 8
cm. What is the magnitude of the magnetic fields at C?
A. 1.04 x10-5 T
B. 2.08 x10-2 T
C. 2.67 x10-6 T
D. 5.0x10-3 T
E. 0.8x10-3 T
22.The figure shows a cross section of three parallel wires each carrying a current of 20 A. The currents in wires A and B are out of the
paper, while that in wire C is into the paper. If the distance R = 5.0 mm, what is the magnitude of the force on a 2.0-m length of wire A?
a.
b.
c.
d.
e.
23 mN
64 mN
32 mN
46 mN
55 mN
4
Physics 121- Common Exam 3
e = 1.6x10-19 C
me = 9.11x10-31kg
µo = 1.26x10-6 T·m/A
Acir = πR2
F=k
q1q 2
r2
E=
C=
P = I 2R
mp = 1.67x10-27 kg
1 eV = 1.6x1019 J
Asphere = 4πR2
Capacitance:
= I ·V
Spring 2013
E=k
P=
Vcyl = πR2L
q
V2
R
r
r
F = qE
r2
ε A
C= 0
d
Q
V
E=
V
d
∑ ( ∆V ) = 0
r r
F = iLxB
dB =
r r
F = qvxB
FB =iLBsinθ
r r
µ o id s xr
4πr 2
Bwire =
F µ o i 1i 2
=
L
2πd
2
Bwire,ins= (
2
∫x
n
= 1/(a − x )
∫ dx / (a
+ x 2 )3/2 = x / (a 2 a 2 + x 2 )
2
Q
t
J=
t
RC
q = Qf ( 1 − e
)
−
i
A
t
RC
I = I 0e
V = i·R
in parallel:
R=ρ
L
A
Req =
t
RC
∆V=Vc( 1 − e
)
−
τ = RC
−
FB = mac
µoi
2πR 2
Q = C· ∆V
ac =
v2
R
crossfield:
)r
Bwire,seg. =
Btor =
d ax
(e ) = ae ax
dx
dx = x n + 1 n + 1
electric field:
q ∆V =∆K
i=
Current:
Bsol = µo·i·n
d(ax n )
= nax n − 1
dx
Useful Integrals:
∫ dx / (a
µoi
2πr
4
πR3
3
∆U = q ∆V
r r
τ = µxB
µ i
Bcoil = N o
2R
d
1
(ln ax ) =
dx
x
∫ dx (a − x)
FB = qvBsinθ
µ = NiA
Vsphere =
in series : Req = R1+R2+…+Rn
1
1
1 -1
(
)
RC circuit: charging:
+
+ ... +
R1 R 2
Rn
t
t
−
−
RC
RC
I = I 0e
discharging:
q = Q 0e
magnetic field:
r r
r
AxB = ( A x B y − A y B x )k
A·B =AxBx + AyBy + AzBy
Acyl = 2πRL
F
q0
k = 8.99x109 Nm2/C2 ε0 = 8.85x10-12 C2/ Nm2
R=
mv
qB
qE = qvB
T=
v=
E
B
µoi
(sin θ 1 − sin θ 2 )
4πr
µ o iN
2πr
Bz =
± αx
Barc =
µoi
θ
4πR
µ o iR 2
2( R 2 + z 2 ) 3 / 2
d
(sin ax ) = a cos(ax )
dx
∫ dx x + a = ln(x + a) ∫ e
2πm
qB
d
(cos ax ) = − a sin(ax )
dx
dx = ± e αx / α
+ x 2 ) = (1/ a ) tan −1 ( x / a )
∫ dx /
a 2 + x 2 = ln( x + a x + x 2 )
∫ x dx / (a
2
+ x 2 )3/2 = −1/ a 2 + x 2
Prefixes: n (nano) = 10-9 , µ (micro) = 10-6 , m (milli) = 10-3 , k (kilo) = 103 , M (mega) = 106
Dot product: a⋅⋅b = a⋅b⋅cos(θ) = axbx + ayby + azbz Cross product: | a x b | = a⋅b⋅sin(θ); c = a x b = (ay⋅bz − az⋅by )⋅i +
(az⋅bx − ax⋅bz )⋅j + (ax⋅by − ay⋅bx )⋅k
5
P