Problem Solving with Electricity

1

• Chapter 22 Electrostatics (electricity at rest)
• Electrical Forces and Charges (Ch 22 pg.
  410-421)
• 1. Electrical forces are much _____________ than
  gravitational forces.
• 2. Electrical forces arise from protons and
  electrons located within the ___________.
• a. Within the atom there is a positively
  charged_______________ (from protons).
• b. This nucleus is surrounded by ______________
  charged electrons. Fig. 22.2
• All electrons are ____________ in mass and charge
  (all protons are identical in mass and charge).
  Protons are nearly ________ times more massive
  than electrons.
• Neutral atoms have ____________ numbers of
  protons and electrons. When an atom gains
  electrons it will become __ charged (called an
  anion). When an atom loses electrons it will
  become __ charged (called a cation)
• 3. Like charges ___________ and opposite charges
  ____________. Fig. 22.1
• Conservation of Charge
• When a piece of rubber is rubbed with a piece of
  fur, electrons transfer from the fur
• and cause the rubber to become __ charged,
  leaving the fur __ charged. Here the
• electrons were not created or destroyed merely
  transferred. Fig. 22.3 pg. 413.
• Electrons cannot be divided into fractions, so
  the charge of an object is in terms of ______
  numbers of electrons that it is deficient or is
  in excess.
• Coulomb's Law F k q1q2/d2 k is a
  proportionality constant 9.00.109 Nm2/C2.

stronger
atom
nucleus
negatively
identical
1833
equal
-

attract
repel
-
integer
2
charged

• Coulomb's law describes the interaction of
  ____________ particles (much like Newton's law of
  gravitation described the interaction of 2
  objects of mass).
• Coulomb's law states that force between charged
  particles varies directly with the __________of
  the charge of the particles (q) and inversely
  with the square of the ______________ between the
  center of the 2 charged particles
• Note that k is much larger than G (6.67.10-11
  Nm2/kg2) from Newton's law
• F Gm1m2/d2this shows that the forces of
  attraction or repulsion are very ______ for
  particles with a charge of 1 Coulomb compared to
  the force of gravitation for the charged
  particles.
• Compare the electrostatic attraction of a proton
  for an electron and the gravitational attraction
  of an electron for a proton.
• Electrostatic Force Gravitational Force
• F kq1q2 / d2 F Gm1m2/d2
• F 9.00.109 Nm2/C2 (1.60.10-19 C)2 F
  6.67.10-11 Nm2/kg2 )(9.11.10-31kg)(1.67.10-27kg)
  
• (5.3.10-11m)2 (5.3.10-11m)2
• F 8.2.10-8 N F 3.6.10-47 N
• Conductors and Insulators
• 1a. Materials through which electrons can move
  easily are called _______________ (metals would
  be an example-good conductors because they
  contain loosely held _________ electrons which
  also makes them good conductors of heat).
• b. Materials through which electrons move with
  difficulty are called insulators (rubber, glass
  etc)

product
distance
large
conductors
valence
3

• Semiconductors contain a non-conductive material
  in crystalline state (germanium
• or silicon) which gains conductivity by ten
  million times when an ________________
• is added which removes an electron from the
  crystal structure. Transistors are made of
• semiconductors.
• Superconductors are certain metals that acquire
  an infinite conductivity at temperatures
• near ______________ zero (0 K or -273 oC),
  some metals have been found to be
• superconductive at temperatures as high as
  100 K or -173 oC.
• Charging by Friction and Contact
• Friction between surfaces will allow for the
  _________ of electrons between materials
• (scuffing shoes across carpet, rubbing a balloon
  on your head). Fig. 22.6 pg. 417.
• 2. Electrons can be transferred between materials
  w/o friction as well (electrons are
• transferred between you and a doorknob when after
  scuffing shoes across the carpet).
• When a charged object is placed in contact with a
  neutral object some of the charge
• will ___________ (called charging by contact) and
  if the object is a good conductor, the charge
  will spread uniformly to all parts of the surface
  (because like charges ______).
• Charging by Induction
• If a charged object is brought near the surface
  of a ________________ (such as a
• metal surface), the electrons of the conducting
  surface will move toward or away from
• the charged object (if the charged object is __,
  the electrons will move toward the
• charged object). See Fig. 22.7 pg. 417 to see
  how 2 neutral conductors can be given

impurity
absolute
transfer
transfer
repel
conductor

induction
4

• 2. A single sphere can be charged if touched when
  charges are separated by induction. See fig 22.8
  pg. 418. Touching the sphere allows for charges
  to flow off of the conductor this is referred to
  as _______________.
• 3. During thunderstorms, water molecules rub past
  each other as they flow upward. The bottom of
  the cloud becomes __ charged and the upper part
  of the cloud __ charged. The electrons may then
  discharge to the __ charged ground. A lightning
  rod will continuously allow charge to leak from
  the clouds to the rod so no major discharge will
  occur (see fig. 22.9).
• Charge Polarization
• When a charged object is brought near an
  insulator, no ______________ are free to move
  within the insulating material. However, the
  atoms or molecules of the material may rearrange
  so as to align themselves with the charged
  object. See fig. 22.11, 12, 13, 14 pg. 420.
• Some molecules contain ends of opposite charge
  which is referred to as electric
  __________(molecules with dipoles are called
  polar molecules). See fig. 22.15 pg. 421

grounding
-



electrons
dipole
5
Coulombs Law

• F kq1q2 / d2
• d
• F is the Force (N-Newtons)
• q is charge (C-coulombs)
• d is distance (m-meters)

6

• 1 While levitating 2 Latex balloons with the
  force, Yoda rubs them over a Younglings hair
  such that the charge acquired by each balloon is
  -2.0.10-6 C. Later he levitates them in the air
  70. cm apart from each other.
• What is the electrostatic force acting between
  the 2 balloons?
• F k q1q2
• d2
• F (9.00.109 Nm2/C2)(2.0.10-6C)2
• (70. cm (1m / 100cm))2
• F 0.073 N
• b. Is this an attractive or repulsive force? Why?
  
• Since each balloon has acquired a negative charge
  but pulling electrons
• off of the Younglings hair, repulsive the force
  will be.

2 While pouring his cereal, Mace Windu sees 2
cereal puffs repel each other with what he takes
to be the force. If the puffs experience an
electrostatic force of 4.10-23 N and are
separated by 0.03 m, what is the charge on each
puff? F kq2/d2 _______ q
v Fd2 / k q ((4.10-23N (0.03m)2/ 9.00.109
Nm2/C2)1/2 q 2.10-18 C
7

• Electric Field
• Although objects are not in contact, they can
  exert a _________ on one another (as we studied
  in gravitation). The space that surrounds a
  ___________ particle is filled with an electric
  field (just as a gravitational field surrounded
  an object with mass). Fig. 22.16 pg. 422.
• a. An electric field is a ___________ quantity
  for it has magnitude (__________) and direction.
  The magnitude of the field can be measured by its
  effect on a _____ charge whose own electric field
  is too small to interfere with the field of
  interest. The field strength on the test charge
  is directly proportional to the ____________
  creating the field on inversely proportional to
  the _______ of the distance from the center of
  the charge creating the field.
• b. Electric fields are represented by
  _____________ which show the direction the field
  of the charged particle would have on a positive
  test charge. See fig. 22.17, 22.18 22.19 pg.
  422-423. As the arrows get farther apart the
  field strength _____________.
• c. Electric field is defined as force per unit of
  _________ on a test charge.
• E F/qo Last section we saw electrical
  force was F k q qo/r2 so E kq/r2
• Electric Shielding
• a. In conducting materials (such as _________)
  charges move easily to the forces that electric
  fields exert. Charges located within a
  conducting surface move easily to the
  _____________ of the conducting material due to
  the repulsive nature of like charges. This
  leaves ___ charge on the inside of the conducting
  material. Fig.22.21 22.22 pg. 425.
• b. The electric field inside of the conducting
  material would be _______. The charges on the
  outside of the conducting material pull
  __________ in all directions on a test charge.
  The field inside of a conducting surface is zero
  regardless of the ________ of the conducting
  material. See figure 22.20 pg. 424.
• c. Therefore, electric fields can be ___________
  by surrounding whatever it is to be shielded from
  an electrical field by surrounding it in a
  conducting material. Because charges exist on
  the surface of a conducting material, sensitive
  electronic circuits can be shielded from external
  electric disturbances by being encased in a
  __________ box.

Electric Fields
force
charged
vector
size
test
charge
square
arrows
decreases
charge
metals
outside
no
zero
equally
shape
shielded
metal
8
1. -4.0 µC 3.0 µC
-7.0 µC 0.20 m
0.15 m
F1
F2 Determine the net force acting upon the 3.0
µC particle. F1 kq1q2 / r2 F1 (9.00.109
Nm2 / C2)(4.0.10-6 C)(3.0.10-6 C) / (0.20
m)2 F1 2.70 N (towards the 4.0 µC
particle) F2 kq1q2 / r2 F2 (9.00.109
Nm2 / C2)(7.0.10-6 C)(3.0.10-6 C) / (0.15
m)2 F2 8.40 N (towards the 7.0 µC
particle) Fnet 8.40 N 2.70 N Fnet
5.7 N towards the -7.0 µC particle
9
Electrical Fields (a measure of Force per charge)

• E F / qo
• F k q qo / r2
• E k q / r2
• E is electrical field (N/C)

10
2.
0.20 m E ?
What is the magnitude and direction of the Field
acting upon the test charge? E k q / r2 E
(9.00.109 N m2/C2)(15.10-6 C) / (0.20 m)2 E
3.4.106 N/C away from the 15 µC particle
11

A more exciting Problem3. Determine where
the net field is zero between the 2 point
charges that are 3.0 m apart.
E1 E2 kq1/ r12 kq2 / r22 (r2 can be d2)
r1/(3.0m r1) r1 (q1/q2)1/2 (3.0m r1) r1
(q1/q2)1/2 (3.0m) - (q1/q2)1/2 r1 r1
(q1/q2)1/2 r1 (q1/q2)1/2 (3.0m) r1 (1
(q1/q2)1/2) (q1/q2)1/2 (3.0m) r1 (q1/q2)1/2
(3.0m) / (1 (q1/q2)1/2) r1(16.10-6C
/4.0.10-6C)1/2 (3.0m) / (1(16.10-6C
/4.0.10-6C)1/2 ) r1 6.00 m/ (12.00) r1 6.00
m / 3.00 r1 2.0 m 2.0 m from the 16 µC
particle
12

A more Problem3. Determine where the net
field is zero between the 2 point charges that
are 3.0 m apart.
E1 E2 kq1/ r12 kq2 / r22 (r2 can be d2)
(q1/q2)1/2 r1/r2 (q1/q2)1/2 r1/(3.0m
r1) (16.10-6C/4.0.10-6C)1/2 r1/(3.0m-r1) 2.00
r1 / (3.0 m r1) 6.00 m 2.00 r1 r1 3.00 r1
6.00 m r1 6.00 m / 3.00 r1 2.0 m or 2.0 m
from the 16 µC particle
13

• Electric Potential Energy and Electric
  Potential
• Recall that work is done when a force moves an
  object in the direction of the force over
  somedistance. An object had a gravitational
  potential energy as a result of being raised to
  certain heights.
• W Fd mgh ?PE
• This potential energy on an object could be
  converted to kinetic energy when released. fig.
  22.23 Work is required to push a charged object
  against an electric field, this work results in
  an
• electrical _______________ energy. See fig.
  22.24 pg. 426. This potential energy can be
  converted to ____________ energy when the charged
  particle is released. ?PE - ?KE If 2
  charges are pushed against the same field
  ________ as much work is required and the 2
  charges will have ____________ the potential
  energy (3 charges would have 3 times the PE).
• Electric Potential measures the Potential energy
  (measured in Joules) per charge (Coulombs) and is
  measured in __________ and is named for Italian
  physicist Allesandro Volta.
• Volts Joules/Coulomb
• A potential of 1000 V would require ________ J of
  energy to move 1 C of charge (this would be
  6.24.1018 electrons) from some distance onto a
  conductor (there are 96,485 C/mol e- or
  1.60.10-19 C/e-). If you were to move 1 mole of
  e- (6.02.1023 electrons), it would require
  96,485,000 J of energy to get 1000 V onto a
  conducting surface. It would only require
  1.60.10-16 J of energy to move 1 electron onto a
  conducting surface to get 1000 V.
• Therefore, a large electric potential may not
  involve large amounts of __________ (that is if
  small amounts of charge are involved). Fig. 22.26
  pg. 428
• Voltage Work / charge (work ?PE or
  ?KE) VW/q

potential
kinetic
twice
twice
volts
1000
energy
14

• Electrical Energy Storage and The Van de Graaff
  Generator
• Electrical energy can be stored in a device
  called a capacitor. A capacitor consists of 2
  oppositely charged plates separated by some
  distance. See fig. 22.27-22.28.
• A discharge of energy can occur when a conductive
  path is provided between the charged plates.
  This
• discharge can be fatal if you are the conducting
  path for high voltages such as the power supply
• for a TV (even after the TV is turned off, the
  energy is still stored between 2 plates)
• thus the warning on such devices
• Capacitors are used beneath each key of a keypad
  (here depressing the key
• ____________ the distance between the
  charged plates so the energy may be released.
  Capacitors are also used in flashbulbs to release
  large amounts of
• energy to produce the flash.
• The Electric Field that exists between the
  charged plates can be described by the following
• Electric field Potential difference/ distance
  between charged plates
• E V/d (V/m or N/C because a volt is a
  N.m/C)
• Capacitance Amount of Charge/Potential
  Difference
• C q/V (Coulombs/ Volt Farad
  symbol F)
• A Van de Graaf generator is a device used to
  produce high ___________ (J/C). Here a large
  hollow metallic sphere draws electrons from
  plates which have acquired electrons from a
  voltage source. (fig. 22.30 )

decreases
voltage
15
Example An electron in Uncle Martins TV is
accelerated toward the screen across a potential
difference of 22,000 V. How much energy does it
lose when it strikes the TV screen and comes to a
halt? (remember work corresponds to a change in
energy)
V w / q
w ?KE
?KE V q
?KE - (22,000 V(1.60.10-19C))
?KE - 3.5.10-15 J
16
Jabba shuffles his body along the dry floor
building up a charge. There is a potential
difference of 9.00.103 V between Jabba and the
chain on Princess Leias neck. A spark jumps
when he is 0.30 cm from the chain. What is the
electric field between Jabba and the chain at
this point?
E V /d
E 9.00.103 V / (0.30 cm
(m/100 cm))
E 3.0.106 V/m
V J/C and J Nm
Or 3.0.106 N /C
If 5.00.10-4 C of charge is stored in the door
knob over a potential difference of 9450 V, what
is the capacitance? C q / V 5.00.10-4 C /
9450 V 5.29.10-8F
17

• F force (N - Newtons) F kq1q2 / r2
• q charge (C - Coulombs) charge of an e- or p
  1.60.10-19 C
• E Electrical Field (N/C or V/m) E F /
  qo kq/r2 V/d
• V Voltage or Potential (V (volts) or J/C)
• V
  w / q (w ?PE or ?KE)
• (large voltages can be (associated with small
• amounts of energy if the charge is small)
• C Capacitance (F (Farad) or C/V) C
  q/V
• µ (micro) 10-6
  k 9.00.109 Nm2/C2

18

• Charging an object can occur by Friction,
  Contact, Induction
• Molecules electrically polarized (getting balloon
  to stick
• to a wall) or they may contain a permanent
  dipole (water)
• Electrical Fields can shielded by encasing
  objects in metal containers.
• A capacitor stores electrical energy between
  oppositely charged plates (a practical example is
  depressing a computer key)
• Charges move to the outside of conducting
  surfaces
• Electrical Fields and Forces are Vector
  quantities
• (have magnitude and direction)