FACULTY OF SCIENCE, WINTER 2008

PHYS 126 LEC B3 : Fluids, Fields and Radiation (Instructor: Marc de Montigny)

Walker, Physics, Chapter 19: Electric Charges, Forces and Fields

• Section 19-1: Electric Charge
  • Electric charge is a characteristic of subatomic particles. It acts as a coupling constant for one of the four fundamental interactions: electromagnetism (click here for a summary of the four fundamental interactions).
    • Unit: Coulomb (C)
    • Charge is quantized as a multiple of the “elementary charge” e = 1.60×10^-19 C.
    • The charge of the electron (fundamental charged particle) is -e.
    • The charge of particles can be a negative multiple of e, zero, or a positive multiple of e.
  • Electric charge is a fundamental conserved property of subatomic particles which determines their electromagnetic interaction.
    • Same-charge particles repel, and opposite-charge particles attract, as shown in Figure 19-2.
    • Figure 19-3 shows the nuclear constituents: electron, m_e = 9.11×10^-31 kg; proton, m_p = 1.673×10^-27 kg; neutron, m_p = 1.673×10^-27 kg.
    • P. 627, Figure 19-4 illustrates charge transfer, during which the total charge is conserved. The nature and amounts of transfered charge is shown in Table 19-1 for different materials.
    • P. 657, Problem 6
  • P. 629 Polarization : is the division of positive and negative in materials which consist of dipoles. See Figure 19-5.
• Section 19-2: Insulators and Conductors
  • Insulators do not allow electrons within them to move from atom to atom.
  • In conductors, each atom gives up one or more electrons that are then free to move throughout the material.
  • Semiconductors have properties intermediate between insulators andn conductors.
  • Superconductors are certain materials which, at extremely low temperatures, are characterized by zero electrical resistance and the exclusion of the interior magnetic field (more about that in later chapters).
• Section 19-3: Coulomb's Law
  • P. 631, Eq. 19-5, Coulomb's Law: F = k |q₁| |q₂|/r² (Magnitude of the electrostatic force between point charges q₁ and q₂, separated by a distance r).
  • P. 631, Eq. 19-6: k = 8.99×10⁹ N•m²/C²
  • Note the similarity with Newton's Law of Universal Gravitation, P. 359, Eq. 12-1: F = Gm₁m₂/r². However, mass is always positive.
  • P. 631 Figure 19-7 illustrates the Coulomb's Law. Keep in mind that Newton's Third Law still applies here.
  • P. 634 Figure 19-8 illustrates the superposition of forces: F₁ = F₁₂ + F₁₃ + F₁₄
  • P. 658, Problem 20
  • P. 637, Eq. 19-7: Q = σA defines the surface charge density σ (Unit: C/m²). (Linear charge density λ (Unit: C/m) is such that Q = λL and the volume charge density ρ (Unit: C/m³) is such that Q = ρV.)
• Section 19-4: The Electric Field
  • P. 638, Eq. 19-9, E = F/q. The electric field is the force per charge.
  • Unit: N/C. Later, we shall express it also as Volt/m.
  • P. 638, Electric field is such that
    • a positive charge experiences a force in the direction of E
    • a negative charge experiences a force in the opposite direction of E
    • the magnitude of the force acting on a charge q is F = |q| E
  • Its gravitational analogue would be E_grav = F_grav/m = mg/m = g
  • P. 639, Eq. 19-10: E = k|q|/r² is the magnitude of the electric field due to a point charge.
  • P. 640 Figure 19-12 illustrates the superposition of fields: E_net = E₁ + E₂
  • P. 658, Problem 34
  • P. 658, Problem 36
• Section 19-5: Electric Field Lines
  • P. 643, Rules for drawing electric field lines. These lines:
    • Point in the direction of the electric field vector at every point.
    • Start at positive charges or at infinity.
    • End at positive charges or at infinity.
    • Are more dense where the electric field has a greater magnitude. The number of lines entering or leaving a charge is proportional to the magnitude of the charge.
  • P. 643 Figure 19-14 represents the field lines for a point charge.
  • P. 644 Figure 19-15 represents the field lines for a system of charges.
  • Simulation
  • P. 659, Problem 46

Section 19-6: Shielding and Charging by Induction

• P. 646: Excess charge (positive or negative) on a conductor moves to the exterior surface of the conductor.
• P. 647: At equilibrium (i.e. charges at rest), the electric field within a conductor is zero.
• P. 647: Electric field lines contact conductor surfaces at right angles.
• P. 647 Figure 19-19 illustrates the previous points.
• P. 648 Figure 19-20 is an illustration that the field is more intense near a sharp point; accordingly, the field lines are more densely packed.
• P. 648 Figure 19-21 is an example of how a conductor shields its interior from external fields, although it does not shield the exterior from the field within it.
• P. 648: A conductor can be charged without direct physical contact with another charged object by a process called charge induction. This is shown in P. 649, Figure 19-22:
  1. A charged rod induces + and - charges on opposite sides of the conductor.
  2. When the conductor is grounded, charges that are repelled by the rod enter the ground. There is now a net charge on the conductor.
  3. Removing the grounding wire, with the rod still in place, traps the net charge on the conductor.
  4. Removing the rod, the conductor retains a charge of opposite sign to that on the charged rod.
• Connecting a conductor to the ground is referred to as grounding. The ground itself is a good conductor and it can give up or receive an unlimited number of electrons.

Section 19-7: Electric Flux and Gauss's Law [OMITTED]

• P. 649, Eq. 19-11: Φ_E = E A cosθ, Definition of Electric Flux
• P. 650, Figure 19-23 shows the electric flux Φ_E (a) when E is perpendicular to the surface (Φ_E = EA is maximal); (b) when E is parallel to the surface (Φ_E = 0); (c) when the perpendicular to the surface is tilted at an angle θelative to E (Φ_E = EA cosθ);

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