Electric Charge, Force, and Field

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Chapter 20

• Electric Charge, Force,and Field

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Properties of Electric Charges

• Two types of charges exist (named by Benjamin
  Franklin) positive and negative
• Like charges repel and unlike charges attract one
  another
• Natures most basic positive charges are the
  protons (held firmly in the nucleus and do not
  move from one material to another)
• Natures most basic negative charges charge are
  the electrons an object becomes charged by
  gaining or losing electrons

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Properties of Electric Charges

• Electric charge is always conserved (not created,
  only exchanged) in an isolated system
• Objects become charged because negative charge
  (electrons) is transferred from one object to
  another
• Charge is quantized (a multiple of a fundamental
  unit of charge, e) electrons have a charge of
  e and protons have a charge of e
• The SI unit of charge is the Coulomb (C)
• e 1.6 x 10-19 C

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Particle Summary
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Coulombs Law

• Electric force is
• Along the line joining the two point charges
• Inversely proportional to the square of the
  separation distance, r, between the particles
• Proportional to the product of the magnitudes of
  the charges, q1 and q2 on the two particles
• k 8.9875 x 109 N m2/C2 Coulomb constant
• Attractive if the charges are of opposite signs
  and repulsive if the charges have the same signs

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Electric Forces

• Electric forces are vector quantities
• Electric force on q1 is equal in magnitude and
  opposite in direction to the force on q2
• Electric force is exerted by one object on
  another object without physical contact between
  them field force
• The superposition principle applies resultant
  force on any one charge equals the vector sum of
  the forces exerted by the other individual
  charges that are present

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Superposition Principle
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Chapter 20Problem 40

• A charge 3q is at the origin, and a charge -2q is
  on the positive x-axis at x a. Where would you
  place a third charge so it would experience no
  net electric force?

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Electric Field

• Electric field exists in the region of space
  around a charged object (source charge)
• When another charged object q0 (test charge)
  enters this electric field, the field exerts an
  electric force F on the test charge
• Electric field
• SI units N / C

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Electric Field

• The field is produced by some charge or charge
  distribution, separate from the test charge
• The existence of an electric field is a property
  of the source charge the presence of the test
  charge is not necessary for the field to exist
• The test charge serves as a detector of the field

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Direction of Electric Field

• The direction of the vector of electric field is
  defined as the direction of the electric force
  that would be exerted on a small positive test
  charge placed at that point
• The electric field produced by a negative charge
  is directed toward the charge (attraction)
• The electric field produced by a positive charge
  is directed away from the charge (repulsion)

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Relationship Between F and E

• If q is positive, the force and the field are in
  the same direction if q is negative, the force
  and the field are in opposite directions
• Coulombs law, between the source and test point
  charges, can be expressed as
• Then

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Superposition of Electric Fields

• At any point P, the total electric field due to a
  group of source charges equals the vector sum of
  the electric fields of all the charges

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Continuous Charge Distribution

• Charge ultimately resides on individual
  particles, so that the distances between charges
  in a group of charges may be much smaller than
  the distance between the group and a point of
  interest
• In this situation, the system of charges can be
  modeled as continuously distributed along some
  line, over some surface, or throughout some volume

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Continuous Charge Distribution

• Divide the charge distribution into small
  elements, each of which contains ?q
• Calculate the electric field due to one of these
  elements at point P

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Continuous Charge Distribution

• Evaluate the total field by summing the
  contributions of all the charge elements

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Charge Densities

• Volume charge density when a charge is
  distributed throughout a volume
• dq ? dV ? Q / V with units C/m3
• Surface charge density when a charge is
  distributed over a surface area
• dq s dA s Q / A with units C/m2
• Linear charge density when a charge is
  distributed along a line
• dq ? dl ? Q / l with units C/m

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Charge Densities

• Linear charge density when a charge is
  distributed along a line
• dq ? dl ? Q / l with units C/m

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Problem-Solving Strategy

• Categorize (individual charge? group of
  individual charges? continuous distribution of
  charges?) and take advantage of any symmetry to
  simplify calculations
• For a group of individual charges use the
  superposition principle, find the fields due to
  the individual charges at the point of interest
  and then add them as vectors to find the
  resultant field
• For a continuous charge distribution a) the
  vector sums for evaluating the total electric
  field at some point must be replaced with vector
  integrals b) divide the charge distribution into
  infinitesimal pieces, calculate the vector sum by
  integrating over the entire charge distribution

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Chapter 20Problem 46

• A 1.0-µC charge and a charge 2.0-µC are 10 cm
  apart. Find a point where the electric field is
  zero.

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Electric Field of a Uniform Ring of Charge
(Example 20.6)
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Electric Field of a Uniformly Charged Disk
(Problem 71)

• The ring has a radius R and a uniform charge
  density s
• Choose dq as a ring of radius r
• The ring has a surface area 2pr dr

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Electric Field of a Uniformly Charged Disk
(Problem 71)
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Motion of Charged Particles

• When a charged particle is placed in an electric
  field, it experiences an electrical force
• If this is the only force on the particle, it
  must be the net force
• The net force will cause the particle to
  accelerate according to Newtons second law
• If the field is uniform, then the acceleration is
  constant
• If the particle has a positive (negative) charge,
  its acceleration is in the direction of
  (opposite) the field

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Particle Summary
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Electric Dipole

• An electric dipole consists of two charges of
  equal magnitude and opposite signs separated by
  2a
• The electric dipole moment p is directed along
  the line joining the charges from q to q and
  has a magnitude of p 2aq
• Assume the dipole is placed in a uniform field,
  external to the dipole (it is not the field
  produced by the dipole) and makes an angle ? with
  the field
• Each charge has a force of F Eq acting on it

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Electric Dipole

• The net force on the dipole is zero
• The forces produce a net torque on the dipole
• t 2Eqa sin ? pE sin ?
• The torque can also be expressed as the cross
  product of the moment and the field

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Electric Dipole
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Classification of Substances vs. Their Ability to
Conduct Electric Charge

• Conductors are materials in which the electric
  charges move freely in response to an electric
  force (e.g., copper, aluminum, silver, etc.)
• When a conductor is charged in a small region,
  the charge readily distributes itself over the
  entire surface of the material
• Insulators (dielectrics) are materials in which
  electric charges do not move freely (e.g., glass,
  rubber, etc.)
• When insulators are charged (by rubbing), only
  the rubbed area becomes charged (no tendency for
  the charge to move into other regions of the
  material)

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Classification of Substances vs. Their Ability to
Conduct Electric Charge

• Semiconductors their characteristics are
  between those of insulators and conductors (e.g.,
  silicon, germanium , etc.)

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An Atomic Description of Dielectrics

• Molecules are said to be polarized when a
  separation exists between the average position of
  the negative charges and the average position of
  the positive charges
• Polar molecules are those in which this condition
  is always present
• Molecules without a permanent polarization are
  called nonpolar molecules
• The average positions of the positive and
  negative charges act as point charges, thus polar
  molecules can be modeled as electric dipoles

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An Atomic Description of Dielectrics

• A linear symmetric molecule has no permanent
  polarization (a)
• Polarization can be induced by placing the
  molecule in an electric field (b)
• Induced polarization is the effect that
  predominates in most materials used as
  dielectrics in capacitors

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An Atomic Description of Dielectrics

• In the absence of an electric field the molecules
  that make up the dielectric (modeled as dipoles)
  are randomly oriented
• An external electric field produces a torque on
  the molecules partially aligning them with the
  electric field alignment of dipoles reduces the
  electric field

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Answers to Even Numbered Problems Chapter 20
Problem 14 1.6 1020
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Answers to Even Numbered Problems Chapter 20
Problem 26 5.2 1011 N/C
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Answers to Even Numbered Problems Chapter 20
Problem 42 (1.6 iˆ - 0.33 jˆ) N or 1.7 N at an
angle of - 11