PHYS1444-003,Fall 05, Term Exam #1, Oct., 12, 2005
Name: Keys
1.
2.
3.
4.
A circular ring of charge of radius and a total charge Q lies in the x-y plane with its
center at the origin. A small positive test charge q is placed at the origin. What is
the direction of the force on q, if Q is negative?
a. is radially outward toward the ring
b. is radially inward from the ring
c. is in the k direction
d. has no direction since the force is zero
Three equal charges are located in the x-y plane with coordinates (0, 3m), (4m, 3m),
and (4m, 0). Which one of the following vector has the direction the same as that of
the force on the charge located at (4m, 3m)?
a. 3i + 4j
b. 4i + 3j
d. 16i + 9j
c. 9i + 16j
What is the direction of the electric field halfway between an electron and a proton?
a. toward the electron
b. toward the proton
c. perpendicular to the line from the electron to the proton
d. undefined since the electric field is zero
Three point charges each equal to 10 µC are located at x = 1m, x = 2m, and x = 3m,
respectively, on the x-axis. What is the magnitude of the electric field at the origin?
a. 2.25 × 10 3 N C
b. 1.23 × 10 5 N C
c. 1.65 × 10 4 N C
d. 2.7 × 10 4 N C
5.
What is the charge per unit length, if a charge of 8.4 µC is evenly distributed
around a ring of radius 0.31 m?
a. 27 µC /m
b. 13.6 µC /m
c. 4.3 µC /m
d. 0.23 µC /m
6.
An amount of charge Q is uniformly distributed over a spherical surface of radius
R. What is the magnitude of the electric field at the center of the sphere?
b. Q 4πε 0 R 2
a. zero
c. Q 8πε 0 R 2
d. this is not possible to determine
7.
If the earth's electric field is 100 N/C downward, what must be the charge on a 1 kg
object so that it would be "weightless" ( 5 points)?
Ans] In order for the object to be “weightless” all the forces exerting on the object must
be balanced. Thus, the gravitational force that pulls the object downward should be
balanced by the electric force between the Earth and the charge on the object.
Fg = Mg = 1kg ⋅ 9.8 m s 2 = 9.8 N ;
Fg = Fe = 9.8 N = 100 q ;
Fe = qE = q100 N C
q = 9.8 × 10 − 2 C
Since the Earth’s electric field is pointing downward, the Earth’s electric charge must be
negative. In order to generate a force that balances the gravitational force, the electric
force must be repulsive. Thus, the object’s charge must be the same as the Earth’s,
negative.
q = − 9.8 × 10 − 2 C
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PHYS1444-003,Fall 05, Term Exam #1, Oct., 12, 2005
8.
If the electric flux through a rectangular area is 5.0 Nm2/C, and the electric field is
then doubled, what is the flux through the area?
a. 2.5 Nm2/C
b. 5.0 Nm2/C
d. 20 Nm2/C
c. 10 Nm2/C
9.
If a charge is located at the center of
through the surface of the sphere is Φ0,
radius of the sphere doubles?
a. 0.125 Φ0
c. Φ0
a spherical volume and the electric flux
what is the flux through the surface if the
b. 0.500 Φ0
d. 8 Φ0
An oxygen ion, O++, is enclosed in a gaussian surface. What is the flux leaving
that surface?
a. 3.2 × 10 −19 Nm 2 C
b. 3.6 × 10 − 8 Nm 2 C
10.
c. 8.86 × 10 − 12 Nm 2 C
11.
d. 2 Nm 2 C
The electric field at all points on a closed surface is 225 N/C outwards. If the area
of the surface is 6.3 m2, what is the net charge enclosed inside the surface?
a. 142 C
b. 36 C
c. 12.6 nC
d. 2 × 10−19 C
A long straight line of charge has a uniform positive charge per unit length λ. The
line is partially enclosed in a long rectangular box of length L and ends of area A,
the line running through the center of each end. What is the electric flux through
the surface of the box? (5 points)
12.
Ans]
G Q
G
Φ 0 = E ⋅ dA =
;
∫
ε0
Q= λ L
G Q
G
λL
Φ 0 = E ⋅ dA =
=
∫
13.
ε0
ε0
Two equal charges Q are separated by a distance d. One of the charges is released
and moves away from the other due to the force between them. When the moving
charge is a distance 3d from the other charge, what is its kinetic energy? (5 points)
Ans]
Ud =
Q2
4πε 0 d
;
U 3d =
Q2
4πε 0 3 d
KE = ∆ U = U d − U 3 d =
2Q 2
4πε 0 3 d
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PHYS1444-003,Fall 05, Term Exam #1, Oct., 12, 2005
14. If the potential at a distance d from a dipole is Vo for distances large compared to
the length of the dipole, then what is the potential at twice the distance from the dipole?
a. also Vo
b. Vo/2
d. Vo/8
c. Vo/4
15.
If the potential is given by V = xy - 3z-2, what is the electric field has a ycomponent?
a. x
b. y
c. x + y
d. x + y - 6z-3
16.
If a molecule of oxygen in air has a translational kinetic energy of 1/40 eV, what is
its speed? Mass of an oxygen molecule is 32.0u. (5 points)
Ans]
E=
v=
1
1
1
1.6 × 10 − 19 J = KE = mv ′ 2
eV =
40
40
2
2 ⋅ 1.6 × 10 − 19
= 388 m / s
40 ⋅ 32 ⋅ 1.66 × 10 − 27 kg
17.
What is the unit of capacitance, the farad, equivalent to?
a. V/m2
b. C/V
c. V/C
d. J/C
18.
A parallel plate capacitor has plates of area 0.40 m2 and plate separation of 0.20
mm. The capacitor is connected to a 9.0 V battery. What is the capacitance of the
capacitor?
b. 20 mF
a. 18 nF
c. 180 µF
d. 18 µF
19.
Parallel plate capacitor #1 has twice the plate area and twice the plate separation of
capacitor #2. What is the capacitance of the second capacitor?
b. double the first
a. the same as the first
c. quadruple the first
d. eight times the first
20.
If the polarity of the voltage applied to a 4.0 nF cylindrical capacitor is reversed,
what is the capacitance?
a. 0.25 nF
b. 4.0 nF
c. -0.25 nF
d. -4.0 nF
21.
A 1 pF capacitor is connected in parallel with a 2 pF capacitor, the parallel
combination then being connected in series with a 3 pF capacitor. What is the
resulting equivalent capacitance?
a. 1.5 pF
b. 3 pF
c. 4.5 pF
d. 6 pF
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PHYS1444-003,Fall 05, Term Exam #1, Oct., 12, 2005
22.
If the voltage on a capacitor is doubled, what happens to the energy stored by the
capacitor?
a. stays the same
b. doubles
d. halves
c. quadruples
23.
Three 4 mF capacitors are connected in series across a 12 V battery. What is the
total energy stored by this combination of capacitors?
a. 24 mJ
b. 96 mJ
c. 288 mJ
d. 1728 mJ
24.
If a dielectric of dielectric constant 4 is inserted between the plates of a parallel
plate capacitor filling the gap, what happens to the capacitance?
a. is unaffected
b. increases by a factor of 4
c. decreases by a factor of 4
d. increases by a factor of 16
25.
If a 10 A current flows for two minutes, how many electrons have passed any point
in the circuit (5 points)?
Ans]
Q = 10 C s ⋅ 2 min = 10 C s ⋅ 120 sec = 1.2 × 10 3 C
Ne =
26.
27.
28.
29.
Q
1.2 × 10 3 C
=
= 7.5 × 10 21
e 1.6 × 10 − 19 C
Which way does the electric current flow through a resistor?
a. from high potential to low potential
b. from low potential to high potential
c. can flow from any potential to any different potential
d. with no direction since it is not a vector
The temperature coefficient, α, of resistivity for copper is 0.0068 oC-1. If a copper
wire has a resistance of 104 Ω at 20 oC, what is its resistance at 80 oC?
a. 42 Ω
b. 71 Ω
d. 161 Ω
c. 146 Ω
A 1200 watt toaster is connected to a 120-V AC line. What is the average power
dissipated?
a. 0 W
b. 1200 W
c. 1700 W
d. 2400 W
Copper has one free electron per atom, a density of 8.9 × 103 kg m3 , and an atomic
mass of 63.5 u. How many free electrons are there in a cubic centimeter of copper?
a. 8 . 4 × 1 0 2 2
b. 4 .3 × 1 0 2 4
c. 5 . 4 × 1 0 2 4
30.
d. 4 .3 × 1 0 3 0
At very low temperatures the resistivity of some materials becomes zero as
indicated by high precision measurements. What is this phenomenon known as?
a. superresistivity
b. supraresistivity
c. superconductivity
d. BSCCO
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PHYS1444-003,Fall 05, Term Exam #1, Oct., 12, 2005
Useful formulae and constants
G
Magnitude of the electric force between two charges: F =
q1 q2
4πε 0 r 2
G
Q
Magnitude of the electric field generated by a charge Q: E =
4πε 0 r 2
U
where U is the electric potential energy.
q
G G Q
E ⋅ dA =
Electric potential: V =
Gauss’ law: Φ = v∫
ε0
b
G
G
Relationship between electric potential and the electric field: Vba = − ∫ E ⋅ dl or
a
∂V
∂V
∂V
Ex =
; Ey =
; Ez =
;
∂x
∂y
∂z
Charge stored in a capacitor with capacitance C due to potential difference V is: Q = CV
Capacitance of a parallel plate capacitor is: C = ε 0
A
d
1
2
Energy stored in a capacitor: U = QV
Ohm’s Law: V = IR
Electric Power: P = IV = I 2 R =
V2
R
Average power of a resistance R in an AC circuit: P = I rmsVrms
l
, ρ the resistivity, A the cross sectional area and L the length.
A
Temperature dependence of a conductor resistivity: ρT = ρ0 ⎡⎣1 + α (T − T0 ) ⎤⎦
Resistance: R = ρ
Permittivity of free space: ε 0 = 8.85 × 10−12 C2 N ⋅ m 2
Charge of an electron: q2 = −e = −1.6 × 10−19 C
Avogadro’s number : N A = 6.02 × 1023 mol-1
Atomic mass unit (1u): 1u = 1.66 × 10 −27 kg
Speed of light: c = 3 × 108 m s
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