Exam
Solution
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Coulomb's
law: Two identical small charged spheres are a certain distance apart, and
each one initially experiences an electrostatic force of magnitude F due to the other.
With time, charge gradually leaks off of both spheres. When each of the spheres has lost
half its initial charge, the magnitude of the electrostatic force will be
A) 1/8 F.
B) 1/2 F.
C) 1/4 F.
D) 1/16 F.
1)
C
-
2) Electric field
of a single point-charge: A metal sphere of radius 10 cm carries a charge of
+2.0 µC uniformly distributed over its surface. What is the magnitude of the electric
field due to this sphere at a point 5.0 cm outside the sphere's surface? (k = 1/4πε0 = 8.99
× 109 N · m2/C2)
A) 4.0 × 107 N/C
B) 4.0 × 105 N/C
C) 4.2 × 106 N/C
D) 8.0 × 107 N/C
E) 8.0 × 105 N/C
2)
3) Multiple point-charges: Two
3)
point charges, Q1 = -1.0 µC and Q2 = + 4.0 µC, are placed
as shown in the figure. (k = 1/4πε0 = 8.99 × 10 9 N · m2/C2) The y component of the
electric field, at the origin O, is closest to
× 103 N/C.
B) -6.0 × 103 N/C.
C) 6.0 × 103 N/C.
D) 7.1 × 103 N/C.
E) -3.8 × 103 N/C.
A) 3.8
→
1
E
C
4) Gauss's
law: Which of the following statements about Gauss's law are correct? (There
may be more than one correct choice.)
A) If there is no charge inside of a Gaussian surface, the electric field must be zero at
points of that surface.
B) Only charge enclosed within a Gaussian surface can produce an electric field at
points on that surface.
→ C) The electric flux passing through a Gaussian surface depends only on the amount
of charge inside that surface, not on its size or shape.
→ D) If a Gaussian surface is completely inside an electrostatic conductor, the electric
field must always be zero at all points on that surface.
E) Gauss's law is valid only for symmetric charge distributions, such as spheres and
cylinders.
4)
5) Gauss's
5)
law: A charge q = 2.00 µC is placed at the origin in a region where there is
^ Calculate the flux of the net electric
already a uniform electric field E = (100 N/C)i.
C ,D
C
field through a Gaussian sphere of radius R = 10.0 cm centered at the origin. (ε0 = 8.85 ×
10-12 C2/N · m2)
A) zero
B) 1.13 × 105 N · m2/C
C) 2.26 × 105 N · m2/C
D) 5.52 × 105 N · m2/C
-
6) Potential energy
of point-charges: Two point charges of +1.0 µC and -2.0 µC are located
0.50 m apart. What is the minimum amount of work needed to move the charges apart to
double the distance between them? (k = 1/4πε0 = 8.99 × 10 9 N · m2/C2)
A) +18 mJ
B) -18 mJ
C) -36 mJ
D) 0 mJ
E) +36 mJ
6)
-
7) Electric field
and potential: In a certain region, the electric potential due to a charge
distribution is given by the equation V(x,y) = 2xy - x2 - y, where x and y are measured in
meters and V is in volts. At which point is the electric field equal to zero?
A) x = 0.5 m, y = 1 m
B) x = 1 m, y = 0.5 m
C) x = 0 m, y = 0 m
D) x = 1 m, y = 1 m
→ E) x = 0.5 m, y = 0.5 m
7)
8) Capacitors
8)
in combination: When two or more capacitors are connected in parallel
across a potential difference,
A) each capacitor carries the same amount of charge.
→ B) the potential difference across each capacitor is the same.
C) the equivalent capacitance of the combination is less than the capacitance of any of
the capacitors.
D) All of the above choices are correct.
E) None of the above choices are correct.
2
A
E
B
9) Capacitors
in combination: Three capacitors are connected as shown in the figure. What
is the equivalent capacitance between points a and b?
A) 7.1
µF
B) 12
µF
C) 8.0
µF
D) 1.7
µF
E) 4.0
9)
D
µF
-
10) Ohm's
law: Calculate the current through a 10.0-m long 22 gauge (having radius 0.321
mm) nichrome wire if it is connected to a 12.0-V battery. The resistivity of nichrome is
100 × 10-8 Ω · m.
A) 61.8 A
B) 17.5 A
C) 776 mA
D) 30.9 A
E) 388 mA
10)
E
-
11)
RC circuits: For the circuit shown in the figure, the switch S is initially open and the
capacitor voltage is 80 V. The switch is then closed at time t = 0. How long after closing
the switch will the current in the resistor be 7.0 µA?
A) 87
s
B) 61
s
C) 78
s
-
3
D) 95
s
E) 69
s
11)
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
12) RC
→
circuits: A resistor and a capacitor are connected in series across an ideal
battery having a constant voltage across its terminals. At the moment contact is
made with the battery
(a) the voltage across the capacitor is
A) equal to the battery's terminal voltage.
B) less than the battery's terminal voltage.
C) greater than the battery's terminal voltage.
D) zero.
12)
(b) the voltage across the resistor is
→ A) equal to the battery's terminal voltage.
B) less than the battery's terminal voltage.
C) greater than the battery's terminal voltage.
D) zero.
13)
13)
Written answer question. Copy neatly the diagram below on a blank sheet of
paper and then answer the following question:
Three charges are arranged on the x-axis as shown in diagram. The charge
at the origin is +2µC. The two charges located at +a and –a are -1µC. Draw the
electric field vectors as arrows at the points indicated by X’s. The arrows should
point in the direction of the electric field, and the length of the arrows should
represent the relative magnitude of the electric field at each location.
4
D
,
A