Chapter 23 Electric Charge and Electric Fields

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Chapter 23 Electric Charge and Electric Fields

• What is a field?
• Why have them?
• What causes fields?

Field Type Caused By
gravity mass
electric charge
magnetic moving charge
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Electric Charge

• Types
• Positive
• Glass rubbed with silk
• Missing electrons
• Negative
• Rubber/Plastic rubbed with fur
• Extra electrons
• Arbitrary choice
• convention attributed to ?
• Units amount of charge is measured in
  Coulombs
• Empirical Observations
• Like charges repel
• Unlike charges attract

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Charge in the Atom

• Protons ()
• Electrons (-)
• Ions
• Polar Molecules

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Charge Properties

• Conservation
• Charge is not created or destroyed, only
  transferred.
• The net amount of electric charge produced in any
  process is zero.
• Quantization
• The smallest unit of charge is that on an
  electron or proton. (e 1.6 x 10-19 C)
• It is impossible to have less charge than this
• It is possible to have integer multiples of this
  charge

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Conductors and Insulators

• Conductor transfers charge on contact
• Insulator does not transfer charge on contact
• Semiconductor might transfer charge on contact

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Charge Transfer Processes

• Conduction
• Polarization
• Induction

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The Electroscope
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Coulombs Law

• Empirical Observations
• Formal Statement

Direction of the force is along the line joining
the two charges
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Active Figure 23.7
(SLIDESHOW MODE ONLY)
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Coulombs Law Example

• What is the magnitude of the electric force of
  attraction between an iron nucleus (q26e) and
  its innermost electron if the distance between
  them is 1.5 x 10-12 m

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Hydrogen Atom Example

• The electrical force between the electron and
  proton is found from Coulombs law
• Fe keq1q2 / r2 8.2 x 108 N
• This can be compared to the gravitational force
  between the electron and the proton
• Fg Gmemp / r2 3.6 x 10-47 N

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Subscript Convention
q1
q2
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More Coulombs Law
q1
q2
Coulombs constant
permittivity of free space
Charge polarity Same sign Force is
right Opposite sign Force is Left
Electrostatics --- Charges must be at rest!
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Superposition of Forces
Q1
Q2
Q0
Q3
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Coulombs Law Example

• Q 6.0 mC
• L 0.10 m
• What is the magnitude and direction of the net
  force on one of the charges?

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Zero Resultant Force, Example

• Where is the resultant force equal to zero?
• The magnitudes of the individual forces will be
  equal
• Directions will be opposite
• Will result in a quadratic
• Choose the root that gives the forces in opposite
  directions

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Electrical Force with Other Forces, Example

• The spheres are in equilibrium
• Since they are separated, they exert a repulsive
  force on each other
• Charges are like charges
• Proceed as usual with equilibrium problems,
  noting one force is an electrical force

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Electrical Force with Other Forces, Example cont.

• The free body diagram includes the components of
  the tension, the electrical force, and the weight
• Solve for q
• You cannot determine the sign of q, only that
  they both have same sign

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The Electric Field

• Charge particles create forces on each other
  without ever coming into contact.
• action at a distance
• A charge creates in space the ability to exert a
  force on a second very small charge. This
  ability exists even if the second charge is not
  present.
• We call this ability to exert a force at a
  distance a field
• In general, a field is defined
• The Electric Field is then

Why in the limit?
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Electric Field near a Point Charge
Electric Field Vectors
Electric Field Lines
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Active Figure 23.13
(SLIDESHOW MODE ONLY)
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Rules for Drawing Field Lines

• The electric field, , is tangent to the field
  lines.
• The number of lines leaving/entering a charge is
  proportional to the charge.
• The number of lines passing through a unit area
  normal to the lines is proportional to the
  strength of the field in that region.
• Field lines must begin on positive charges (or
  from infinity) and end on negative charges (or at
  infinity). The test charge is positive by
  convention.
• No two field lines can cross.

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Electric Field Lines, General

• The density of lines through surface A is greater
  than through surface B
• The magnitude of the electric field is greater on
  surface A than B
• The lines at different locations point in
  different directions
• This indicates the field is non-uniform

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Example Field Lines
Line Charge
Dipole
For a continuous linear charge distribution,
Linear Charge Density
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Active Figure 23.24
(SLIDESHOW MODE ONLY)
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More Field Lines
Surface Charge Density
Volume Charge Density
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Superposition of Fields
q1
q2
0
q3
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Superposition Example

• Find the electric field due to q1, E1
• Find the electric field due to q2, E2
• E E1 E2
• Remember, the fields add as vectors
• The direction of the individual fields is the
  direction of the force on a positive test charge

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Electric Field of a Dipole (ex. 23.6)
y
-q
q
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P23.19

• Three point charges are arranged as shown in
  Figure P23.19.
• Find the vector electric field that the 6.00-nC
  and 3.00-nC charges together create at the
  origin.
• (b) Find the vector force on the 5.00-nC charge.

Figure P23.19
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P23.52

• Three point charges are aligned along the x axis
  as shown in Figure P23.52. Find the electric
  field at
• the position (2.00, 0) and
• the position (0, 2.00).

Figure P23.52
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FIG. P23.52(a)
in x direction.


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P23.19

(a)

(b)
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Continuous Charge Distributions
Single piece of a charge distribution
Single charge
Continuous charge distribution
Discrete charges
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Finding dq
Cartesian
Polar
Line charge
Surface charge
Volume charge
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Example Infinitely Long Line of Charge


y-components cancel by symmetry






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Example Charged Ring (ex 23.8)
y-components cancel by symmetry







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Check a Limiting Case
When
The charged ring must look like a point source.
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Uniformly Charged Disk (ex. 23.9)
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Binomial Expansion Theorem
Quadratic terms and higher are small
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Two Important Limiting Cases
Large Charged Plate
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Parallel Plate Capacitor
Q
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Motion of Charged Particles in a Uniform Electric
Field
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Example

• A proton accelerates from rest in a uniform
  electric field of 500 N/C. At some time later,
  its speed is 2.50 x 106 m/s.
• Find the acceleration of the proton.
• How long does it take for the proton to reach
  this speed?
• How far has it moved in this time?
• What is the kinetic energy?

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Motion of Charged Particles in a Uniform Electric
Field
Q
-e
-Q
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Active Figure 23.26
(SLIDESHOW MODE ONLY)
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Motion of Charged Particles in a Uniform Electric
Field
Phosphor Screen
This device is known as a cathode ray tube (CRT)
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Summary
Point Charges
Coulombs Law
Electric Field
These can be used to find the fields in the
vicinity of continuous charge distributions
Line of Charge
Dipole
Charged Plate