PHYSICS 212
CHAPTER 16
ELECTRICAL ENERGY AND CAPACITANCE
WORKBOOK
ANSWERS
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INSTRUCTIONS
1. Turn this workbook in on time for credit, even if it is not complete. (No credit
if late.)
2. Complete this workbook neatly. Do not write in ink so that corrections can be
made. (Credit will be lost if this is turned in messy.)
3. Complete the chapter outline section as early as possible. Don’t wait for the due
date to be assigned to start.
4. Complete the sections in sequence.
5. Study and learn definitions of terms, physical quantities, units, principles, and
basic equations before attempting problems.
6. You may work on this with other students but do not copy another student’s
workbook or let a student copy this workbook. Do not copy from other sources
either.
7. Wherever possible, include diagrams in your solutions. Diagrams are required.
8. Keep this workbook after it is graded and returned to you.
9. Using the answer key, redo all questions and problems until you can answer
them all correctly by yourself without help.
10. Use the workbook to learn the general problem-solving strategy rather than
how individual problems are solved.
PHYSICS 212 CHAPTER 16 OUTLINE
ELECTRICAL ENERGY AND CAPACITANCE
16.1
Potential Difference and Electric Potential
Is the force between electric charges conservative or non-conservative?
CONSERVATIVE
How is the change in potential energy of an electric charge related to the work done on the charge as
it moves under the influence of a Coulomb force?
Explain equation 16.1 and state its limitations.
Equation 16.1 relates a particle’s change in potential energy as it moves in an
electric field.
Limitation: It is valid only if the electric field is a uniform electric field.
How is electric potential defined?
Electric potential is the potential energy per unit electric charge.
What are the SI units of electric potential?
Volts (V)
16.2
Electric Potential and Potential Due to Point Charges
Write equations 16.4, list and name each variable and state its SI units.
V = electric potential at a radial distance r from point charge q.
16.3
Potentials and Charged Conductors
What is true of the electric potential on the surface of a charged conductor in electrostatic
equilibrium?
The surface of a conductor in electrostatic equilibrium is an equipotential surface.
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How much work must be done moving an electric charge for point A to point B if points A and B
have the same electric potential?
What is true of the electric potential everywhere inside a charged conductor in electrostatic
equilibrium?
The electric potential everywhere inside a conductor in electrostatic equilibrium is
constant.
Define the physical quantity known as the electron volt.
The electron volt is the energy gained or lost by an electron traversing a potential
difference of one volt.
16.4
Equipotential Surfaces
Define the term equipotential surface.
An equipotential surface is the collection of points in space which have the same
electric potential.
What is the relation between electric field lines and equipotential surfaces?
Electric field lines are perpendicular to equipotential surfaces.
16.5
Applications
How is electric potential related to electrostatic precipitators and to Xerography?
A high voltage is used to charge particles and attract them an oppositely charged
plate or wire.
16.6
Capacitance
How is capacitance defined?
Capacitance is the ability to maintain a charge separation across a potential
difference.
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What are the SI units of capacitance?
Farads (F)
16.7
The Parallel-Plate Capacitor
Write equations 16.9, list and name each variable and state its SI units.
C = capacitance, F
A = plate area, m2
eo = permittivity of free space, C2/Nm2
d = plate separation, m
Draw a sketch of a parallel-plate capacitor. Include in the sketch where positive charge will be,
where negative charge will be, how the electric field is oriented, and show what the variables A and
d measure. Try to give your diagram a 3D perspective.
16.8
Combinations of Capacitors
What symbol is used in a circuit diagram to represent a capacitor?
What symbol is used in a circuit diagram to represent a battery?
Draw a circuit diagram of two capacitors in series.
Draw a circuit diagram of three capacitors in parallel.
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Write equations 16.12, list and name each variable and state its SI units.
Ceq = equivalent capacitance, F
C1 ... = individual capacitances in parallel, F
Write equations 16.15, list and name each variable and state its SI units.
Ceq = equivalent capacitance, F
C1 ... = individual capacitances in series, F
16.9
Energy Stored in a Charged Capacitor
Write equations 16.17, list and name each variable and state its SI units.
Q = stored charge, C
C = capacitance, F
V = potential difference between plates, V
16.10 Capacitors with Dielectrics
What is a dielectric material?
A dielectric material is an insulating material whose molecules have a dipole moment
or can have a dipole moment induced on them.
What does the dielectric constant of a material measure?
The dielectric constant is a measure of the degree to which the electric fields of the
molecules of a dielectric material counter-align with an external electric field.
What are the SI units of the dielectric constant?
There are none, it has no units.
If an empty capacitor has capacitance Co, what will its new capacitance be when a dielectric material
of dielectric constant ko is inserted between its plates?
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What does the physical quantity dielectric strength measure?
The dielectric strength of a material is the maximum internal electric field it can have
before it begins to break apart and become conducting.
How are the units V/m related to N/C?
These two sets of units are equivalent.
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PHYSICS 212 CHAPTER 16 MULTIPLE CHOICE QUESTIONS
ELECTRICAL ENERGY AND CAPACITANCE
B____1.
The unit of electrical potential, the volt, is dimensionally equivalent to:
A. J×C.
D. F×C.
B. J/C.
E. J/F.
C. C/J.
C____2.
The quantity of electrical potential, the volt, is dimensionally equivalent to:
A. force/charge.
D. electric field/distance.
B. force ´ charge.
E. charge ´ distance.
C. electric field ´ distance.
B____3.
A free electron is in an electric field. With respect to the field, it experiences a force acting:
A. parallel.
B. anti-parallel (opposite in direction).
C. perpendicular.
D. along a constant potential line.
E. none of the above is correct in the general case.
A____4.
In which case does an electric field do positive work on a charged particle?
A. a negative charge moves opposite to the direction of the electric field.
B. a positive charge is moved to a point of higher potential energy.
C. a positive charge completes one circular path around a stationary positive charge.
D. a positive charge completes one elliptical path around a stationary positive charge.
E. a negative charge moves in the direction of the electric field.
C____5.
If the distance between two negative point charges is increased by a factor of three, the resultant
potential energy is what factor times the initial potential energy?
A. 3.0
D. 1/9
B. 9.0
E. 1
C. 1/3
E____6.
Which of the following characteristics are held in common by both gravitational and electrostatic
forces when dealing with either point masses or charges?
A. inverse square distance law applies
B. forces are conservative
C. potential energy is a function of distance of separation
D. charge and mass of isolated systems are conserved
E. all of the above choices are valid
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C____7.
Consider two charged spheres, one with charge +2 C and the other with -2 C. A proton (a
positively charged particle) is at the point halfway between the spheres. What is not zero?
A. the potential energy of the proton
B. the work to move the proton from infinity to that point
C. the force on the proton
D. the dipole moment of the proton
E. all of the four above are zero
A____8.
An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it
hits the screen. What is the kinetic energy of the electron in electron volts? (1 eV = 1.6 ´ 10-19 J)
A. 1.0 ´ 104 eV
D. 6.25 ´ 1022 eV
15
B. 1.6 ´ 10 eV
E. 2.5 ´ 1023 eV
C. 1.6 ´ 10-22 eV
D____9.
Electrons in an x-ray machine are accelerated from rest through a potential difference of
50 000 V. What is the kinetic energy of each of these electrons in eV?
A. 50 eV
D. 50 keV
B. 80 eV
E. 80 keV
C. 330 eV
D___10.
At which location will the electric field between the two parallel plates of a charged capacitor be
the strongest in magnitude?
A. near the positive plate
B. near the negative plate
C. midway between the two plates at their ends
D. midway between the two plates nearest their center
E. anywhere between the two plates
D___11.
The unit of capacitance, the farad, is dimensionally equivalent to which of the following?
A. V/C
D. C/V
B. V×C
E. V/J
C. J/V
D___12.
Increasing the voltage across the two plates of a capacitor will produce what effect on the
capacitor?
A. increase charge
D. decrease capacitance
B. decrease charge
E. decrease charge and increase capacitance
C. increase capacitance
B___13.
A 0.25-mF capacitor is connected to a 400-V battery. Find the charge on the capacitor.
A. 1.2 ´ 10-12 C
D. 0.020 C
B. 1.0 ´ 10-4 C
E. 0.010 C
C. 0.040 C
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B___14.
If two parallel, conducting plates have equal positive charge, the electric field lines will:
A. leave one plate and go straight to the other plate.
B. leave both plates and go to infinity.
C. enter both plates from infinity.
D. be parallel to both plates.
E. none of the above.
D___15.
A 20-mF capacitor is attached across a 1000-V power supply. What is the net charge on the
capacitor?
A. 10 mC
D. 80 mC
B. 20 mC
E. none of the above
C. 40 mC
D___16.
Increasing the separation of the two charged parallel plates of a capacitor, which are disconnected
from a battery, will produce what effect on the capacitor?
A. increase charge
D. decrease capacitance
B. decrease charge
E. decrease charge and increase capacitance
C. increase capacitance
A___17.
If three 4.0-:F capacitors are connected in parallel, what is the combined capacitance?
A. 12 mF
D. 0.46 mF
B. 0.75 mF
E. 5.5 mF
C. 8.0 mF
C___18.
Inserting a dielectric material between two charged parallel conducting plates, originally separated
by air and disconnected from a battery, will produce what effect on the capacitor?
A. increase charge
D. decrease capacitance
B. increase voltage
E. decrease voltage
C. increase capacitance
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PHYSICS 212 CHAPTER 16 ADDITIONAL QUESTIONS
ELECTRICAL ENERGY AND CAPACITANCE
Include diagrams wherever possible.
1.
What is the potential energy of a 5 mC charge placed at an electric potential of 1000 V?
2.
Calculate the electric potential 15 cm from a metal sphere whose radius is 5 cm and has a net charge of
-2.5 mC.
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3.
A 10 mC charge is placed at x = 0 and a 5 mC charge is placed at x = 3cm. These two charges are fixed
in place. If a charged particle with charge 2 mC and mass 3 mg is placed at x = 6 cm, what will its
speed be after it has moved 2 cm? Redo this problem for a similar particle with a charge of -2 mC.
Charges q1 and q2 are fixed in place as shown. When the particle is placed at point A and released
from rest, it will be repelled and move to point B, 2 cm from A (and actually keep moving.) The
solution requires using the work-energy theorem because the charged particle is moving in a nonuniform electric field created by two point charges.
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4.
(A) Calculate the capacitance of two circular conducting plates each of radius 10 cm held parallel to
each other and 3 mm apart. (B) What would the capacitance be if the area between the plates is filled
with a material of dielectric constant 3.4?
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5.
A 2.5 mf capacitor is connected to a 150 V power supply. What charge is stored in this capacitor?
6.
A 5cm radius conducting sphere with a net charge of 10 mC is next to a 10 cm radius conducting
sphere of net charge 5 mC. The centers of the spheres are 20 cm apart. If the two spheres are
momentarily connected by a conducting wire, what force will exist between them after the wire is
removed? [Hint: How many conducting surfaces are there while the spheres are connected?]
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PHYSICS 212 CHAPTER 16 PROBLEMS
ELECTRICAL ENERGY AND CAPACITANCE
PRACTICE PROBLEMS:
HOMEWORK PROBLEMS:
3, 7, 13, 25, 32, 35, 39, 45, 49, 58
1, 5, 12, 16, 19, 22, 26, 30, 34, 43, 47
Include diagrams wherever possible.
1.
A proton moves 2.00 cm parallel to a uniform electric field of E = 200 N/C. (a) How much work is
done by the field on the proton? (b) What change occurs in the potential energy of the proton? (c)
What potential difference did the proton move through?
(a) The work done is
(b) The change in the electrical potential energy is
(c) The change in the electrical potential is
5.
The potential difference between the accelerating plates of a TV set is about 25 kV. If the distance
between the plates is 1.5 cm, find the magnitude of the uniform electric field in the region between the
plates.
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12.
Two point charges are on the y-axis, one of magnitude 3.0 × 10!9 C at the origin and a second of
magnitude 6.0 × 10!9 C at the point y = 30 cm. Calculate the potential at y = 60 cm.
where
, and
Thus,
16.
A point charge of 9.00 × 10!9 C is located at the origin. How much work is required to bring a positive
charge of 3.00 × 10!9 C from infinity to the location x = 30.0 cm?
The potential at distance
from a charge
Thus, the work required to carry a charge
is
from infinity to this location is
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19.
In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha
particles (having charges of +2e and masses of 6.64 × 10!27 kg) were fired toward a gold nucleus with
charge +79e. An alpha particle, initially very far from the gold nucleus, is fired at 2.00 × 107 m/s
directly toward the nucleus, as in Figure P16.19. How close does the alpha particle get to the gold
nucleus before turning around? Assume the gold nucleus remains stationary.
Figure P16.19
From conservation of energy,
, which gives
or
22.
(a) How much charge is on each plate of a 4.00-:F capacitor when it is connected to a 12.0-V battery? (b) If
this same capacitor is connected to a 1.50-V battery, what charge is stored?
(a)
(b)
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26.
A 1-megabit computer memory chip contains many 60.0 × 10!15 -F capacitors. Each capacitor has a plate area of
21.0 × 10!12 m2 . Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration).
The diameter of an atom is on the order of 10!10 m = 1 Å. Express the plate separation in angstroms.
, so
30.
Three capacitors, C1 = 5.00 :F, C2 = 4.00 :F, and C3 = 9.00 :F, are connected together. Find the effective
capacitance of the group (a) if they are all in parallel, and (b) if they are all in series.
(a) For parallel connection,
(b) For series connection,
, giving
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34.
Consider the combination of capacitors in Figure P16.34. (a) What is the equivalent capacitance of the group?
(b) Determine the charge on each capacitor.
Figure P16.34
(a) The combination reduces to an equivalent capacitance of
(b)
From Figure 2,
and
Then, from Figure 1,
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in stages as shown below.
43.
A parallel-plate capacitor has 2.00-cm2 plates that are separated by 5.00 mm with air between them. If a 12.0-V
battery is connected to this capacitor, how much energy does it store?
The capacitance is
and the stored energy is
47.
A capacitor with air between its plates is charged to 100 V and then disconnected from the battery. When a
piece of glass is placed between the plates, the voltage across the capacitor drops to 25 V. What is the dielectric
constant of the glass? (Assume the glass completely fills the space between the plates.)
The initial capacitance (with air between the plates) is
dielectric inserted) is
, and the final capacitance (with the
where Q is the constant quantity of charge stored on the plates.
Thus, the dielectric constant is
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