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Transcript
```Physics 9: Static Electricity
A.
Electric Nature of Matter (16-1 to 16-4)
1. subatomic particles
a. summary chart (Coulomb, C, unit of charge)
particle
Proton
Neutron
Electron
mass (kg)
1.67 x 10-27
1.67 x 10-27
9.11 x 10-31
charge (C) +1.60 x 10-19
0
-1.60 x 10-19
b. + and – attract (+ and + or – and – repel)
c. attraction between protons and electrons holds
matter together/apart explains Fs, Ff, Fn, etc.
2. conductors and insulators
a. metals are conductors because valence electrons
are loosely held by individual atoms and can travel
from atom to atom (excess charge on a conductor
spreads out on the outside surface)
b. non-metals are insulators because valence
electrons are restricted to individual atoms
(excess charge on an insulator stays localized)
c. metalloids (semiconductors) are intermediate
between metals and nonmetals
3. adding static charge to insulators
a. rubbing dissimilar insulators together transfers
electrons from one to the other
b. excess electrons = negatively charged
deficient electrons = positively charged
c. total charge is unchanged (conservation of charge)
4. adding static charge to conductors
a. conduction: charged conductor contacts neutral
conductor; electrons flow until equal electric
potential (water tanks analogy)
b.
B.
induction
1. neutral conductor is connected to the earth
by a grounded wire (a)
2. charged conductor approaches the neutral
conductor, but doesn’t touch, so that
electrons flow away from the charged
conductor and down into the earth (b)
3. excess charge spreads evenly over surface (c)
Electric Force and Field (16-5 to 16-9)
1. electric force, Fe = k|qQ|/r2 (N)
a. charges Q and q or Q1 and Q2 in (C)
b. k = 1/(4єo) = 9.0 x 109 N•m2/ C2
c. єo = 8.85 x 10-12 C2/N•m2
1. permittivity of free space
2. measures the degree that an electric field is
"permitted" in a vacuum
d. r is distance between Q's from center to center
e. charge sign is not included in calculation, but is
used to determine direction of Fe
f. similar to Fg = -GMm/r2, except electric force can
attract (–) or repel (+)
Name __________________________
2.
electric field, E = k|Q|/r2 (N/C)
a. Michael Faraday's concept is useful to explain
forces at a distance, where space around –Q is
curved inward so that +q is drawn in as if it were
pulled (no physical contact is necessary)
+q
r
-Q
b.
c.
electric field lines (lines of force)
1. lines directed into cone show direction of field
2. away from +Q and toward –Q
3. perpendicular to the conductor's surface
4. (concentric rings are equipotential lines, V,
which are discussed in the next section)
oppositely charged plates
edge effect
E=0
E is constant (except edge effect) E kQ/r2
E = 0 inside a conductor (hollow or solid;
charged or uncharged)
solving E and Fe from multiple charges problems
(determining the magnitude and direction of the solid
line at point p)
1.
2.
3.
E1 E2
• 
+Q1




4.





p
–Q2
determine E1and E2, at position, p, due to Q1 and Q2:
determine direction of E1 and E2 (+), –))
o same direction: Etot = E1 + E2
o opposite direction: Etot = E1 – E2
o right angles: Etot = (Ex-tot2 + Ey-tot2)½, tan = Ey/Ex
determine the electric force on q at point p
o magnitude, Fe = |q|Etot
o direction

+q: Fe is in the same direction as E

–q: Fe is in the opposite direction as E
solve x where E = 0 problems
D
Q1
Q2
location is closer to weaker charge
like charges (x < D), unlike charge (x > D)
(|+Q1| > |+Q2|): kQ1/x2 = kQ2/(D – x)2; solve for x
(|+Q1| > |–Q2|): kQ1/x2 = kQ2/(x – D)2; solve for x
math shortcut: take the square root of both sides
before cross multiplying
C.
Electric Potential Energy and Voltage (17-1 to 17-5)
1. potential energy between point charges, Q and q
a. Ue = kqQ/r (J)
b. Ue = 0, when Q and q are infinitely far apart
c. scalar quantity
d. sign of charge is included in calculation
e. analogous to gravitational potential energy
1. Ug = -GMm/r (Ug = 0 when r = )
m into negative Ug
2. electric potential (also called "potential" or "voltage")
due to point charge Q
a. V = kQ/r (V)—volt
b. is relative to where V = 0
1. infinitely far from a point charge (theoretical)
2. practical to set earth as V = 0 ("ground")
c. letter V has three uses (confusing!)
1. voltage (electric potential) = V
2. potential difference, V = V
3. volt = V
3. solving V and Ue from multiple charges problems
(determine the value of the dashed line at point p)
V1 + V2
•
+Q1



4.


5.
p
–Q2
determine V1 and V2 at position p, due to Q1 and Q2:
add the voltages together, Vtot = V1 + V2
determine electric potential energy for charge q at
point p: Ue = qVtot
solve x where V = 0 problems
D
+Q1
–Q2
only meaningful for unlike charges (between charges
and closer to weaker charge)
(|+Q1| > |–Q2|): kQ1/x = kQ2/(D – x); solve for x
cathode ray tube
a. device for accelerating a beam of electrons
(cathode rays)—video monitors
b.
c.
design
1. high voltage used to charge two plates
2. electrons accelerate from cathode (– plate) to
anode (+ plate)
3. anode has small opening into evacuated tube
calculating the velocity of the electrons: |Ue| = K
 |qe(Vhigh – Vlow)| = ½mev2
me = 9.11 x 10-31 kg
qe = 1.6 x 10-19 C
Capacitor (17-7 to 17-9)
1. battery connected to parallel conducting plates fills
plates with opposite, but equal, charges
a. Vplates = Vbattery
b. charge can't pass directly from one plate to the
other so plates remain charged when battery is
removed
c. stores charge and energy
2. electric field, E = V/d (NOT kQ/r2)
a. solid arrows
b. constant
c. V/m = N/C
3. equipotentials, V
a. all points at the same V
b. dashed lines
c. perpendicular to E
d. decrease evenly with d
e. analogous to elevation
lines on contour map
4. capacitance, C =єoA/d (F)
a. "capacity" to store charge
b. єo = 8.85 x 10-12 C2/N•m2
c. A = common area of plates
d. d = distance between plates
5. stored charge, Q = CV
a. charge increases as voltage increase
Q
slope = C
Work = Area under line = Uc
V
potential energy, Uc = ½QV
Steps
Algebra
W = ½bh
substitute Q for h and V for b
W = ½QV
Uc = ½QV
substitute Uc for W
Uc = ½CVV = ½CV2
substitute CV for Q
Uc = ½C(Q/C)2 = ½Q2/C
substitute Q/C for V
6. variable capacitor
a. connect/disconnect voltage source (battery)
1. connected: voltage V is constant
2. disconnected: charge Q is constant
b. increase/decrease area A or distance d
Capacitance
Battery
Variable
Connected
Disconnected
Capacitor
C = єoA/d
Q =C x V
Q = C x V






A












d






7. uses
a. RAM memory (charged = 1, uncharged = 0)
b. computer keyboard (variable capacitor—d)
c. camera flash (energy/charge storage)
d. heart defibrillator (energy/charge storage)
constant
b.
constant
D.
(2) Graph the sums and draw a smooth curve from
x = 0 to 20 m, skipping 5 m and 15 m.
V (V)
Experiments
1.
Static Charge Lab
a. Work in pairs. Each student charge a piece of plastic
tape as directed. Hold the piece of tape by the end so
that it hangs down from your hand. Bring the two
pieces of tape toward each other.
(1) What do you observe?
9
8
7
(2) Explain what happened.
6
5
4
b.
Work in pairs. Place two pieces of plastic tape on top of
each other and charge them as directed. One student
pull off the top piece of tape and the other student pull
off the bottom piece. Hold the tape as before and bring
the two pieces of tape toward each other.
(1) What do you observe?
3
2
1
0
(2) Explain what happened.
2.
Plotting Electric Potential Lab
a. Q1 = +1 x 10-9 C and Q2 = +1 x 10-9 C.
(1) Add Q1 + Q2 for each position x = 0 to 20 m and
fill in the sums in the column Q1 + Q2.
x (m)
Q1 (V)
Q2 (V)
Q1+ Q2 (V)
Q1 + -Q2 (V)
0
1.80
0.60
1
2.25
0.64
2
3.00
0.69
3
4.50
0.75
4
9.00
0.82
2
4
6
8
10
12 14
16
18
x (m)
(3) Is there a location where the graph crosses the xaxis? If so this is where V = 0.
(4) Locate where the slope of the graph equals zero;
this is where E = 0.
b.
Q1 = +1 x 10-9 C and Q2 = -1 x 10-9 C.
(1) Subtract Q1 – Q2 for each position x = 0 to 20 m
and fill in the differences in the column Q1 + -Q2.
(2) Graph the differences and draw a smooth curve
from x = 0 to 20 m except 5 m and 15 m.
V (V)
8
6
4
5
6
9.00
1.00
7
4.50
1.13
8
3.00
1.29
9
2.25
1.50
10
1.80
1.80
11
1.50
2.29
12
1.29
3.00
13
1.13
4.50
14
1.00
9.00
16
0.82
9.00
17
0.75
4.50
18
0.69
3.00
19
0.64
2.29
20
0.60
1.80
15
2
0
-2
-4
-6
-8
2
4
6
8
10
12
14
16
18
x (m)
(3) Locate where the graph crosses the x-axis; this is
where V = 0.
(4) Is there a location where the slope of the graph
equals zero? If so this is where E = 0.
Practice Problems
1.
A. Electric Nature of Matter
A positively charged rod is brought close to a neutral
conducting sphere. What is the charge on A?
++++++++++++++++++
A
(A) positive
(B) negative
(C) neutral
Questions 2-3 A positively charged rod is brought close to two
neutral conducting spheres connected by a wire.
++++++++++++++++++
2.
3.
4.
A
B
The wire is disconnected, and then the rod is removed.
What are the charges on A and B?
(A) +A, -B
(B) -A, +B
(C) both neutral
The rod is removed first, and then the wire is disconnected.
What are the charges on A and B?
(A) +A, -B
(B) -A, +B
(C) both neutral
Consider the two ways to charge a conductor.
a. Label the picture that illustrate conduction and the
picture that illustrates induction
b.
What could be done to make the metal rod in the right
side set of pictures have a net negative charge?
5.
A neutral glass rod is rubbed with a neutral piece of silk.
The rod acquires an excess charge of + 1 C. What is the
excess charge on the piece of silk?
6.
A positively charged piece of metal is used to charge a
neutral piece of metal. Which technique, conduction or
induction, can make the neutral metal?
positively charged
negatively charged
B. Electric Force and Field
Question 7-12 Sphere B is r meters from sphere A, which has a
charge of +1 C. The electric force between them is 1 N.
A
7.
r
14. When the proton and electron are released, they move
(A) away from each other (B) toward each other
15. How does the electric force change as they move?
(A) increase
(B) same
(C) decrease
16. The acceleration of the electron compare to the proton is
(A) greater
(B) equal
(C) less
17. At which position will the proton and electron collide?
(A) 1
(B) 2
(C) 3
Questions 18-21 Sphere A, Q = +1 C and m = 0.4 kg, is
suspended from the ceiling near a charged Wall. Forces
F1, F2 and F3 act on A.
 53o

F1
B
What is the direction of the force on B if QB = +1 C?
(A) 
(B) 
8. What is the magnitude of the force on B if QB = +2 C?
(A) ¼ N
(B) ½ N
(C) 2 N
(D) 4 N
9. What is the magnitude of the force on A if QB = +2 C?
(A) ¼ N
(B) ½ N
(C) 2 N
(D) 4 N
10. What is the magnitude of the force on B if QA = QB = +2 C?
(A) ¼ N
(B) ½ N
(C) 2 N
(D) 4 N
QA = QB = +1 C
11. What is the magnitude of the force on B if r is doubled?
(A) ¼ N
(B) ½ N
(C) 2 N
(D) 4 N
12. What is the magnitude of the force on B if r is halved?
(A) ¼ N
(B) ½ N
(C) 2 N
(D) 4 N
Questions 13-17 An electron and proton are 1 m apart.
p 1
2
3 e
13. The proton's electric force compared to the electron is
(A) greater
(B) equal
(C) less
F2
A
F3
18. What the charge on the wall?
(A) positive
(B) negative
19. What is F3?
(A) 3 N
(B) 4 N
(C) 5 N
20. What is F1?
(A) 3 N
(B) 4 N
(C) 5 N
21. What is F2?
(A) 3 N
(B) 4 N
(C) 5 N
Questions 22-24 The electric field strength is E at point p,
which is r distance way from sphere A with charge +Q.
+Q
•p
22. What is the direction of the electric field at p?
(A) 
(B) 
23. If Q is doubled, what is the electric field at point p?
(A) ¼E
(B) ½E
(C) 2E
(D) 4E
24. If r is doubled, what is the electric field at point p?
(A) ¼E
(B) ½E
(C) 2E
(D) 4E
Questions 25-27 What is the direction of the electric field at point
p half way between charges of equal magnitude?
25.
+Q 
•p
+Q
(A) 
(B) 
(C) E = 0
26.
+Q 
•p
–Q
(A) 
(B) 
(C) E = 0
27.
–Q 
•p
+Q
(A) 
(B) 
(C) E = 0
Questions 28-31 Where is the electric field equal to zero?
28. A
+4Q
B
C
–Q
D
29.
A
–4Q
B
C
30.
A
+Q
B
C
–Q
+4Q
–4Q
D
D
31. A
+Q
B
C
D
Questions 32-34 What is the direction of electric field at point p?
32.
+Q 
•p
 +Q
(A) 
(B) 
(A) 
 –Q
(B) 
(C) 
–Q 
•p
(A) 
(B) 
33.
34.
(C) 
+Q 
•p
(D) 
(D) 
 –Q
(C) 
(D) 
Questions 35-37 What is the direction of the field at point p, which
is in the center of the box?
35.
–Q
+Q
•p
–Q
+Q
(A) 
(B) 
(C) 
(D) E = 0
36.
+Q
+Q
•p
+Q
+Q
(A) 
(B) 
(C) 
(D) E = 0
37.
+Q
–Q
•p
–Q
+Q
(A) 
(B) 
(C) 
(D) E = 0
38. In a simplified model of a hydrogen atom, an electron
orbits a proton at a distance of 5.3 x 10-11 m.
a. What is the electric force between the electron and
proton?
b.
What is the gravitational force between the electron
and proton? (G = 6.67 x 10-11 N•m2/kg2)
b.
What is the charge on each sphere if the mass of each
sphere is 0.030 kg?
41. What is the strength of an electric field inside a conductor?
42. Where is the net charge located on a good conductor?
43. What is the orientation of the electric field with respect to a
conductor's surface?
44. The electric field lines are drawn around charged spheres
and plates. Indicate whether the charged spheres or
plates are positive or negative.
a.      
b.
 
 

     
45. A 50 C charge and a 1 C charge are 0.1 m apart.
a. Which charge generates the stronger field at 0.1 m?
b.
Which charge exerts the greater force on the other?
46. What is the electric field 3 m away from a +10C charge?
c.
What is the velocity of the electron in its orbit?
39. Two small identical metal spheres contain excess charge
of -10 C and +8 C, respectively ( = 10-6). The spheres
are 0.4 m apart.
a. Determine the magnitude and direction of the force
between the spheres.
The spheres touch and then returned to their original 0.4-m
separation.
b. Determine the charge on each sphere.
c.
Determine the magnitude and direction of the force
between the spheres.
47. Determine the magnitude and direction of the electric field
at point p.
Q1 = -5 C
Q2 = +10 C
•
p
1m
3m
48. Determine the magnitude and direction of the electric field
at point p.
Q1 = -5 C
Q2 = +10 C
1m
p•
3m
40. Two charged spheres of equal mass and charge,
suspended from a common point by threads that are 0.5 m
long, rest a distance of 0.5 m apart.
a. Label the three forces acting on the
right sphere (Fg, Ft, Fe) on the vector
30o
sum diagram below.
0.5 m
49. Determine the magnitude and direction of the electric field
at the center of a square 2 m on an edge if charges of +8
C each are at three of the corners of the square.
+8C
2m
+8C
2m
+8 C
50. What is the magnitude and direction of the electric force on
a -3 x 10-7 C charge in a 500 N/C electric field directed
toward the west?
51. Calculate the magnitude and direction of the force on Q2.
Q1 = +10 C Q2 = +2 C
Q3 = -10 C
0m
5m
b.
What is the electric force on the +32 C charge?
c.
Which charge generates the stronger field at a point
half way between the two charges?
d.
Determine the magnitude and direction of the electric
field at the midpoint.
15 m
A -1 C charge is placed at the midpoint
e. Determine the magnitude and direction of the electric
force on the -1 C charge at the midpoint.
52. A +40 C and -10 C charge are 10 m apart.
+40 C
-10 C
f.
0m
10 m
a. Determine the magnitude and direction of the electric
field at a point half way between.
b.
Determine where the -1 C charge can be placed
where it would experience a net electric force of zero.
59. A proton traveling at 3 x 106 m/s enters a region where the
electric field has a magnitude of 3 x 105 N/C. The electric
field is uniform and slows the proton's motion. Determine
a. the acceleration on the proton.
Determine where the electric field is zero.
53. A drop of water has a net charge of 150 electrons. What is
its mass if it is suspended in an electric field is 300 N/C?
b.
the distance the proton will travel before coming to a
momentary halt.
54. A particle of mass 1 x 10-6 kg has an excess charge of
+1 C. The particle is located in a region between two
oppositely charged parallel plates where the electric field is
uniform and has a magnitude of 1000 N/C. Determine the
a. the force acting on the particle.
c.
the time required for the proton to travel this distance.
b.
60. Q1 = +9 C, and Q2 = +1 C, are located on the x-axis at
x = 0 m and x = 6 m, respectively.
Q1 = +9 C
Q2 = +1C
the acceleration of the particle.
The plates are 0.01 m apart and the particle is initially at
rest at a point close to the positive plate.
c. Determine the velocity of the particle "just" before it
strikes the negative plate.
0m
6m
a. Determine where a third charge, Q3 = +1 C, can be
placed and experience no net force.
b.
Charge Q2 is replaced with a -1 C charge located at
x = 6 m. Determine where a third charge, Q3 = +1 C,
can be placed and experience no net force.
55. What is the electric field 5 m away from a +10C charge?
56. What is the electric force between an electron and proton
that are 1.0 x 10-10 m apart?
57. What is the magnitude and direction of the electric force on
a +5 x 10-7 C charge in a 200 N/C electric field directed
toward the west?
58. A +32 C and +8 C charge are 2 m apart.
+32 C
+8C
0m
2m
a. What is the electric force on the +8 C charge?
C. Electric Potential Energy and Voltage
61. A proton and electron are released within a constant
electric field generated between parallel plates.
p
+
–
e
Which has more kinetic energy when it reaches the plate?
(A) electron
(B) proton
(C) tie
62. Which system has +Ue?
+– + +
– –
A
B
C
(A) A
(B) B
(C) C
(D) B and C
63. Which pair of equal charges takes positive work to bring
together from a very large initial distance apart?
+–
+ +
A
B
(A) A
(B) B
(C) A and B
Questions 64-66 Consider the square with four equal charges on
the corners.
+– + +
+ –
75. What is the voltage at 25 cm from a 10-C charge?
76. a.
+– + +
– +
A
B
C
64. Which arrangement has V > 0 at the center?
(A) A
(B) B
(C) C
(D) none
65. Which arrangement(s) is V = 0 at the center?
(A) A
(B) B
(C) C
(D) A and C
66. Which arrangement(s) is V = 0 and E = 0 at the center?
(A) A
(B) B
(C) C
(D) A and C
Questions 67-69 A charge particle is placed at point p in the
electric field, whose direction is indicated by the dashed
arrows. The particle is moved along equal length paths
indicated by the solid arrows.
A
68.
69.
70.

C
p
Which path increases Ue for a positively charged particle?
(A) A
(B) B
(C) C
(D) B and C
Which path decreases Ue for a negatively charged particle?
(A) A
(B) B
(C) C
(D) B and C
Which path does not change Ue for any charged particle?
(A) A
(B) B
(C) C
(D) B and C
Which point(s) have the same potential as point X around
these two equal put opposite charges?
X•
A•
1
2
3
4
b.
Graph E and V on the same grid.
E and V
8000
6000
B
67.
Calculate the electric field E and voltage V from 1 m to
4 m from Q (1 C).
r (m)
E
V
B•
C•
(A) A
(B) B
(C) C
(D) all above
71. What is the potential energy between a -1-C charge and
a +10-C charge that are 25 m apart?
4000
2000
0
c.
1
3
r (m)
Draw a tangent to the V vs. r graph at r = 3 m and
compare its slope with the value of E and 3 m.
77. a.
Determine the voltage at point p, which is at 1 m.
-5 C
+10 C
p
1m
3m
b.
How much work is required to bring an electron from
infinitely far away to point p?
(1) In joules
72. A +2-C charge is infinitely far away from a +20-C charge.
a. What is the electric potential energy?
(2) in eV (q = -1—measured in terms of electrons)
The +2-C charge is moved to 2 m from the +20-C charge.
b. What is the electric potential energy now?
c.
c.
How much work is needed to move the +2-C charge
from infinity to 2 m from the +20-C charge?
Determine the voltage at point p, which is located as
shown
-5 C
+10 C
1m
3m
p
73. Q1 (+10 C) is 10 m from Q2 (-1 C).
a. What is the electric potential energy?
Q1 accelerates to a distance of 2 m from Q2.
b. What is the electric potential energy now?
c.
What is the velocity of Q1 (0.2 kg) at 2 m from Q2?
74. What is the voltage between points if 10 J of work is
required to move 5 C from one point to the other?
78. A +40-C charge and a -10-C charge are 10 m apart.
+40 C
-10 C
a.
0m
10 m
Calculate the voltage at a point half way between.
b.
Determine where the voltage is zero.

79. An electron accelerates through a voltage of 750 J/C.
a. What is the change in the electric potential energy?
b.
85. Two point charges, q1 (3.0 C) and q2 (-1.5 C), are placed
0.30 m apart on the x-axis.
What is the velocity of the electron?
80. 1 electron that moves from 10 V to 20 V in an electric field.
a. The electron (gains or loses) potential energy.
b. What is the change in potential energy (in eV)?
81. Four charged have the same magnitude Q, but two are
positive and two are negative.
+Q
–Q
+Q
–Q
–Q
+Q
+Q
–Q
Arrangement 1
Arrangement 2
In the center of which arrangement is
the electric field equal to zero
the voltage equal to zero
82. Consider the three pairs of charges in the figures below
(1)
(2)
(3)
Has positive potential energy
Has negative potential energy
Requires the most work to separate
83. What is the potential at the center of a 1-m square for each
situation below?
Q1
1m
Q2
1m
a.
Q3
Q1 = Q2 = Q3 = +10 C?
b.
Q1 = Q2 = +10 C and Q3 = -25 C?
a.
Determine the x-coordinate of the point on the line
between the two charges where V = 0.
b.
How much work must be done by an external force to
bring an electron from infinity to the point where V = 0?
D. Capacitor
Questions 86-93 The capacitor with capacitance C has plate
area A, plate separation d, potential difference V, charge Q
and potential energy Uc.
A
V
d
86. What is the charge if the voltage goes from V to 2V?
(A) ¼Q
(B) ½Q
(C) 2Q
(D) 4Q
87. What is the potential energy if the voltage goes from V to 2V?
(A) ¼Uc
(B) ½Uc
(C) 2Uc
(D) 4Uc
88. What is the capacitance if the area goes from A to 2A?
(A) ¼C
(B) ½C
(C) 2C
(D) 4C
89. What is the capacitance if the separation goes from d to 2d?
(A) ¼C
(B) ½C
(C) 2C
(D) 4C
90. The battery remains connected and the plate separation
goes form d to 2d. What happens to the voltage?
(A) ½V
(B) V
(C) 2V
(D) 0
91. The battery remains connected and the plate separation
goes form d to ½d. What happens to the charge?
(A) ½Q
(B) Q
(C) 2Q
(D) 0
92. The battery is disconnected and the plate area goes from
A to 2A. What happens to the charge?
(A) ½Q
(B) Q
(C) 2Q
(D) 0
93. The battery is disconnected and the plate area goes from
A to 2A. What happens to the voltage?
(A) ½V
(B) V
(C) 2V
(D) 0
94. Highlight the correct option for the following capacitor.
A
84. Consider the arrangement of charges below.
A•
B•
40 cm
30 cm
40 cm
60 cm
52 cm
a.
Q1 = +50 C
Q2 = -50 C
Calculate the voltage at point A due to the two charges.
B
Plate (A or B) has the higher electric potential.
The dashed lines are (equipotentials or electric field).
The solid arrows are (equipotentials or electric field).
Each dashed line equals 5 V. The potential difference
between the two plates is (0, 5, 10 or 20) V.
e. The plates are 0.01 m apart. The electric field is
(1000, 2000, 4000 or 8000) V/m.
95. A 330-pF (p = 10-12) capacitor is connected to a 12 V battery.
a. How much charge is stored on the capacitor?
a.
b.
c.
d.
b.
b.
Calculate the voltage at point B due to the two charges.
How much energy is stored in the capacitor?
96. A capacitor stores 10 C when charged with 12 V.
a. What is the capacitance?
b.
How much energy does the capacitor store?
e.
What vertical velocity do the electrons acquire while
passing through the vertical deflection plates?
97. Millikan, an American physicist, determined the charge of
an electron by suspending an oil drop in midair with an
electric field.
f.
How much time does it take the beam to travel from
the vertical deflection plates to the fluorescent screen
if there is 22 cm between them?
g.
What is the vertical displacement of the bright spot on
the fluorescent screen?
a.
What is the force of gravity on the oil drop if it has a
mass of 2.8 x 10-15 kg?
b.
What is the electric field strength between the plates if
the plates have a potential difference of 340 V and a
separation of 1.0 cm?
c.
What charge is necessary to suspend the oil drop
between the two plates?
d.
How many excess electrons are on the oil drop?
98. A cathode ray tube is diagramed below. The heater
current causes electrons to leave the cathode and
accelerate toward the anode, where they pass through a
small opening. Then the beam of electrons, cathode rays,
are turned horizontally by the horizontal deflection plates
and turned vertically by the vertical deflection plates, so
that they form a bright spot on the fluorescent screen. The
moving bright spot and the alternation of on and off
generate an image on a TV picture tube.
a.
How much kinetic energy do the emerging electrons
have if they are accelerated horizontally by 7.0 kV?
b.
What is the velocity of the emerging electrons?
c.
What vertical acceleration do the emerging electrons
experience if a 2.9 x 105 N/C electric field exists
between the vertical deflection plates?
d.
How much time does it take the beam to cross the
vertical deflection plate if it is 2.8 cm long?
Practice Multiple Choice
Briefly explain why the answer is correct in the space provided.
1. Gravitational forces differ from electrostatic forces in that
gravitational forces are
(A) attractive only
(B) repulsive only
(C) both attractive and repulsive
2.
A positive charge of 1 x 10-6 C is placed on an insulated
solid conducting sphere. Which is true?
(A) The charge resides uniformly throughout the sphere.
(B) The electric field inside the sphere is constant in
magnitude, but not zero.
(C) An insulated metal object acquires a net positive charge
when brought near to, but not in contact with, the sphere.
(D) When a second conducting sphere is connected by a
conducting wire to the first sphere, charge is transferred
until the electric potentials of the two spheres are equal.
3.
If the distance separating an electron and a proton is
halved, the electric force between them will be
(A) unchanged
(B) quartered
(C) doubled
4.
Forces between two objects which are inversely
proportional to the square of the distance between the
objects include which of the following?
I. Gravitational force between two celestial bodies
II. Electrostatic force between two electrons
III. Spring force between two masses
(A) I only
(B) II only (C) III only (D) I and II only
5.
Metal sphere A has a charge of -2 units and an identical
metal sphere, B, has a charge of -4 units. If the spheres
are brought into contact with each other and then
separated, the charge on sphere B will be
(A) 0 units (B) -3 units (C) -2 units (D) +4 units
Questions 6-7 Two ⅓-kg metallic spheres, A and B, are 0.3 m
apart. The charge on each sphere is +1.0 x 10-6 C.
6.
0.3 m
What is the electric force between the two charged spheres?
(A) 0.1 N
(B) 0.3 N
(C) 0.25 N (D) 1.0 N
7.
Which arrow represents the direction of the electric field at
point P due to the charges on spheres A and B?
(A) 
(B) 
(C) 
(D) 
8.
In the diagram, P is a point near a negatively charged sphere.
16. An electron e and a proton p are simultaneously released
from rest in a uniform electric field E.
At a later time the electron and the proton will have the same
(A) direction of motion
(B) speed
(C) displacement
(D) magnitude of force
What is the direction of the electric field at point P?
(A) 
(B) 
(C) 
(D) 
17. The hollow metal sphere is positively charged. Point C is
the center and point P is any other point within the sphere.
9.
Two metal spheres, A and B, have charges of +2 x 10-6 C
and +1 x 10-6 C, respectively.
The electric force on A due to B is 2.4 N. What is the
electric force on B due to A?
(A) I.2 N
(B) 4.8 N
(C) 2.4 N
(D) 9.6 N
Questions 10-11 An electron placed between oppositely charged
parallel plates A and B moves toward plate A. The electric
field strength between the two plates is 3,000 N/C.
Which is true of the electric field at these points?
(A) It is zero at both points.
(B) It is zero at C, but is directed inward at P.
(C) It is zero at C, but is directed outward at P.
(D) It is zero at P, but is not zero at C.
18. What is the electric field 2-m from the center of a 1-m hollow
metal sphere, which carries a charge of 4 x 10-6 C?
(A) 9.0 x 103 N/C
(B) 1.8 x 104 N/C
(C) 2.4 x 104 N/C
(D) 3.6 x 104 N/C
19. Where is the electric field closet to zero?
QA = 4 C
QB = -1 C
A
B
C
D
10. What is the direction of the electric field between the plates?
(A) toward plate A
(B) toward plate B
11. What is the force on the electron?
(A) 4.8 x 10-16 N
(B) 2.4 x 10-16 N
-16
(C) 6.4 x 10 N
(D) 1.2 x 10-16 N
12. Which of the following is true about the net force on an
uncharged conducting sphere in a uniform electric field?
(A) It is zero.
(B) It is in the direction of the field.
(C) It is in the direction opposite to the field.
20. Charges -Q and +Q are located on the x- and y-axes,
respectively, each at a distance d from the origin 0.
What is the direction of the electric field at the origin 0?
(A) 
(B) 
(C) 
(D) 
Questions 21-22 Point P is 0.5 m from a charge of -5 x 10-6 C.
13. An electron is accelerated from rest by an electric field that
exerts a force of 8.0 x 10-15 N. What is the the electric field?
(A) 8.0 x 10-24 N/C
(B) 9.1 x 10-22 N/C
(C) 8.0 x 10-6 N/C
(D) 5.0 x 104 N/C
21. The intensity of the electric field at point P is most nearly
(A) 1.8 x 105 N/C
(B) 3.6 x 105 N/C
(C) 1.8 x 106 N/C
(D) 7.2 x 106 N/C
14. Which location will have the greatest electric field strength
as measured from the center of a positively charged hollow
(A) 0
(B) 3/4R
(C) 5/4R
(D) 2R
A second charge, q2 = 1 x 10-6 C is placed at point P.
22. What is the electric force on q2 at point P?
(A) 1.8 N
(B) 0.18 N (C) 3.6 N
(D) 0.09 N
15. Point B is twice as far away from +Q as point A.
23. Two charges, QA = -4 C and QB = +1 C are 6 m apart.
The ratio of the electric field strength at point A to the
electric field strength at point B is
(A) 8 to 1 (B) 4 to 1 (C) 2 to 1 (D) 1 to 1
0m
6m
Where is the electric field equal to zero?
(A) 2 m
(B) 4.8 m (C) 8 m
(D) 12 m
24. Two identical spheres each with a mass of ⅓-kg and
charge of +1.0 x 10-6 C are 0.30 m apart. When the
spheres are released, what is their initial acceleration?
(A) 0.1 m/s2
(B) 0.3 m/s2
(C) 0.25 m/s2
(D) 1.0 m/s2
25. Two identical conducting spheres are charged to +2Q and
-Q, respectively, and are separated by a distance d. The
magnitude of the force of attraction on the left sphere is F1.
After the two spheres are made to touch and then
separated by distance d, the magnitude of the force on the
left sphere is F2. Which of the following is correct?
(A) 2 F1 = F2
(B) F1 = F2
(C) F1 = 2 F2
(D) F1 = 8 F2
26. The figure shows two particles, each with a charge of +Q,
which are located at the opposite corners of a square of
side d.
31. If 60 J of work is required to move 5 C of charge between
two points in an electric field, what is the potential
difference between these points?
(A) 5 V
(B) 60 V
(C) 12 V
d. 300 V
32. How much electrical energy is required to move a 4 x 10 -6-C
charge through a potential difference of 36 V?
(A) 9.00 x 106 J
(B) 1.44 x 10-4 J
(C) 144 J
(D) 1.11 x 10-7 J
Questions 33-34 Point P is 0.5 m from a charge of -5 x 10-6 C.
33. The electric potential (voltage) at point P is most nearly
(A) -2.5 x 104 V
(B) -2.5 x 103 V
(C) -9.0 x 104 V
(D) -1.8 x 103 V
34. A second charge, q2 = 1 x 10-6 C is placed at point P. What
is the electric potential energy of q2 at point P?
(A) -1.8 J (B) -0.18 J (C) -3.6 J (D) -0.09 J
What is the electric force on a particle of charge +q that is
held at point P?
(A) Zero
(B) √2kqQ/d2
(C) kqQ/d2
(D) 2kqQ/d2
Questions 27-30 A charge Q1 = -16 x 10-6 C is on the x-axis at
+4 m, and a charge Q2 = +9.0 x 10-6 C is on the y-axis at +3 m.
Questions 35-36 Two conducting plates are 0.04 m apart. The
lower plate is at a potential of 2 V and the upper plate is at a
potential of 10 V. Point P is 0.01 m above the lower plate.
35. The electric potential at point P is
(A) 10 V
(B) 8 V
(C) 6 V
(D) 4 V
36. The electric field at point P is
(A) 800 V/m (B) 600 V/m (C) 400 V/m (D) 200 V/m
27. What are the electric fields due to Q1 and Q2 at the origin?
(A) E1 = 9,000 N/C and E2 = 9,000 N/C
(B) E1 = 36,000 N/C and E2 = 27000 N/C
(C) E1 = 3,000 N/C and E2 = 4,000 N/C
(D) E1 = 18,000 N/C and E2 = 8,000 N/C
28. The overall strength of the electric field at the origin is
(A) 18,000 N/C
(B) 13,000 N/C
(C) 15,000 N/C
(D) 5,000 N/C
A charge, Q3 = -4 x 10-6 C is placed at the origin.
29. What is the direction of the electric force on Q3?
(A) 
(B) 
(C) 
(D) 
30. What is the electric force on Q3?
(A) 0.05 N (B) 0.5 N
(C) 0.75 N
(D) 2.0 N
Questions 37-40 Determine the charge Q', Voltage V', and
capacitance C' when a capacitor with capacitance C,
attached to a battery with voltage V and filled with charge Q
is altered. Use the options to answer the questions.
C'
Q'
V'
C'
Q'
V'
(A) C
Q
V
(B) ½C Q
2V
(C) 2C
2Q
V
(D) 4C
Q
¼V
37. The battery is disconnected and then the separation
between the plates is doubled.
38. The battery remains connected and the plate area doubles.
39. The battery remains connected and the plate area and
plate separation doubles.
40. The battery is disconnected and then the plate area is
doubled and the plate separation is halved?
41. Two charges, QA = -4 C and QB = +1 C are 6 m apart.
Where is the electric potential, voltage, equal to zero?
(A) 2 m
(B) 4.8 m (C) 8 m
(D) 12 m
42. The capacitance of a parallel-plate capacitor can be
increased by increasing which of the following?
(A) The distance between the plates
(B) The charge on each plate
(C) The area of the plates
(D) The voltage across the plates
Practice Free Response
1.

43. A parallel-plate capacitor is connected to a battery. The
electric field between the plates is 2,000 N/C. If the
voltage is doubled and the distance between the plates is
reduced to 1/5 the original distance, the new electric field is
(A) 1,600 N/C
(B) 2,400 N/C
(C) 5,000 N/C
(D) 20,000 N/C
a.
Questions 44-47 Two ⅓-kg metallic spheres, A and B, are
separated by a distance of 0.3 m. The charge on each
sphere is +1.0 x 10-6 C.
0m
0.3 m
44. Other than at an infinite distance away, where is the
electric potential, voltage, equal to zero?
(A) to the left of A
(B) to the right of B
(C) between A and B
(D) at no location
45. What is the electric potential, voltage, at the midpoint?
(A) 45,000 V
(B) 90,000 V
(C) 135,000 V
(D) 120,000 V
46. What is the electric potential energy of the two sphere system?
(A) 0.02 J (B) 0.05 J (C) 0.03 J (D) 0.15 J
47. The spheres are released. What is the velocity of each
sphere when they are infinitely far apart?
(A) 0.1 m/s
(B) 0.3 m/s
(C) 0.25 m/s
(D) 1.0 m/s
48. A particle of charge Q and mass m accelerates from rest
through a potential difference V attains a velocity v and
kinetic energy K. What is the velocity, v', and kinetic
energy, K', of a particle of charge 2Q and mass 2m that is
accelerated from rest through the same potential
difference?
v'
K'
v'
K'
(A) ½v
¼K
(B) ¼v
½K
(C) 2v
K
(D) v
2K
49. The figure shows two particles, each with a charge of +Q,
which are located at the opposite corners of a square of
side d.
What is the potential energy of a particle of charge +q that
is held at point P?
(A) Zero
(B) √2kqQ/d
(C) kqQ/d
(D) 2kqQ/d
A 0.04-kg conducting sphere, carrying a charge of -30 C, is
suspended by a string at an angle,  = 37o, between two
parallel plates of a capacitor that are 0.2 m apart.
2.
0.2 m
What is the electric force on the sphere?
b.
What is the magnitude and direction of the electric
field between the plates?
c.
What is the voltage between the plates?
Two conducting spheres, A (+9 C, 0.01 kg) and B (-1 C,
0.01 kg) are placed 3 m apart.
A (+ 9 C)
B (-1 C)
a.
0m
3m
What is the electric force between them?
b.
the electric potential energy.
Sphere B is released and accelerates toward sphere A.
c. What is the magnitude and direction of the acceleration?
Determine the following for sphere B when it is 1 m from A.
d. the potential energy.
e.
the kinetic energy.
f.
the velocity.
Sphere B is returned to its original position 3 m from
sphere A. Determine
g. What is the magnitude and direction of the electric
field at the midpoint?
h.
the voltage at the midpoint.
i.
Where is the electric field equal to zero?
j.
where the voltage equals zero.
Sphere C (+6 C, 0.004 kg) is placed at the midpoint.
k. Determine the magnitude and direction of the electric
force on sphere C.
The battery remains attached to the capacitor while the
distance between the plates is doubled.
d. Determine the new capacitance and charge.
l.
The distance is returned to 0.01 m and the battery is
disconnected. Now the area of the plates is doubled.
e. Determine the new capacitance and voltage.
Determine the electric potential energy of sphere C.
m. Sphere C is released from the midpoint. Determine the
velocity of C when it is infinitely far away.
6.
3.
Two charges, Q1 = +5 C and Q2 = -5 C, are located on
the y-axis at y = +3 m and y = -3 m, respectively.
y
In a CRT monitor, electrons are first accelerated from rest
through a high voltage in an electron gun. They then pass
between deflecting plates before striking the screen.
deflection plates
screen
electron gun
0.012 m
d
+3m
+5 C
0
|
4m
x
a.
0.04 m
0.5 m
Determine the voltage in the electron gun that
accelerates an electron to a velocity of 6.0 x 107 m/s.
-5 C
-3 m
Determine the magnitude and direction of the electric field
on the x-axis at x = 4 m.
4.
c.
the acceleration of the electron while it is in the electric
field between the plates.
d.
the time that the electron is between the plates.
e.
the vertical velocity of the electron as it leaves the plates.
f.
the distance, d, where the electron strikes the screen,
which is 0.5 m from the deflection plates.
Two point charges, q1 and q2, are placed 0.30 m apart on
the x-axis. Charge q1 has a value of -3.0 x 10-9 C. The net
electric field at point P is zero.
a.
5.
The deflecting plates are 0.012 m apart, 0.04 m long and
have a 600-V potential between them. Determine
b. the electric field between the plates.
b.
Calculate the magnitude of charge q2.
c.
Calculate the magnitude of the electric force on q2 and
indicate its direction.
A capacitor consists of two metal plates that are separated
by 0.01 m and have cross sectional areas of 0.2 m2.
a. Determine the capacitance?
The capacitor is connected to a 50 V battery.
b. Determine the charge.
c.
Determine the energy.
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