Electrostatics Notes

Atoms

  • Basic building blocks of life.
  • Composed of subatomic particles:
    • Protons (+) - Located in the nucleus.
    • Neutrons (no charge) - Located in the nucleus.
    • Electrons (-$) - Orbit the nucleus.
  • Carbon atom example:
    • 6 protons
    • 6 neutrons

Valence Electrons

  • Outer electrons of an atom.
  • Determine the bonding properties of the atom.

Excited Electrons

  • Absorption and Emission of Radiation
  • Absorption: electron absorbs a photon and moves to a higher energy level.
  • Emission: electron emits a photon and moves to a lower energy level.

Types of Atoms

  • Hydrogen (H)
    • 1 electron
  • Helium (He)
    • 2 electrons
  • Lithium (Li)
    • Additional electron shell compared to hydrogen and helium.
  • Beryllium (Be)
  • Boron (B)
  • Carbon (C)

Electricity

  • Flow of electrons.
  • Electrons flow due to attraction and repulsion forces.

Elementary Charges

  • Protons and electrons have an electric charge, resulting in attractive force.
    • Attraction: positive to negative.
    • Repulsion: positive to positive, negative to negative.

Electric Charge

  • Unit of charge: Coulomb (C).
  • Symbol for charge: "q".
  • Charge of 1 electron: 1.6 \times 10^{-19} C
  • 1 C = 6.25 \times 10^{18} electrons.
  • Smallest charge is generally 1.6 \times 10^{-19} C. You can't have fractional charges like 0.8 \times 10^{-19} C.

Electrostatics

  • Study of stationary charges.
  • Charge is not created or destroyed, but transferred from one object to another.

Everyday Coulombs

  • Phone charger: typically rated at 1 Ampere, meaning 1 C of charge flows per second.
  • Static electricity: charges from rubbing materials together are typically a few microcoulombs.
  • Lightning bolt: typically around 15 C, but can be 350 C for large bolts.
  • Typical alkaline AA battery: about 5 kC = 5,000 C from fully charged to discharged.

Electrons in Charge Examples

  • 1 C: 6.25 \times 10^{18} electrons
  • 2 C: 12.5 \times 10^{18} electrons
  • 5 C: 3.125 \times 10^{19} electrons

Charge of Electrons Examples

  • 6.25 \times 10^{18} electrons: 1 C
  • 1.875 \times 10^{19} electrons: 3 C
  • 5 electrons: 8 \times 10^{-19} C

Coulomb's Law

  • Describes the electric force between two particles.
  • Formula: F = k \frac{q1 q2}{r^2}
    • F_E = electric force
    • q = particles with charge
    • r = distance between charges
    • k = Coulomb's constant (k = 9 \times 10^9 Nm^2/C^2)

Comparison to Gravitational Force

  • Electric force equation: FE = k \frac{q1 q_2}{r^2}
  • Gravitational force equation: Fg = G \frac{Me m_m}{r^2}

Example Calculation of Electric Force

  • Two small spheres:
    • Charge 1: 1.5 nC (1.5 \times 10^{-9} C)
    • Charge 2: -2.0 nC (-2.0 \times 10^{-9} C)
    • Separated by a distance of 1.5 cm (0.015 m).
  • Calculation:
    • FE = k \frac{q1 q_2}{r^2} = (9 \times 10^9) \frac{(1.5 \times 10^{-9})(-2.0 \times 10^{-9})}{(0.015)^2} = -1.2 \times 10^{-4} N
    • Force is attractive because the charges have opposite signs.

Triboelectric Series

  • Lists materials in order of their tendency to gain or lose electrons.
  • Materials higher on the list tend to become positively charged.
  • Materials lower on the list tend to become negatively charged.
  • Examples:
    • Positive end: Air, Human body, Glass, Nylon, Wool, Lead, Cotton, Aluminum, Paper, Steel
    • Negative end: Wood, Gelatin, Nickel, copper, Gold, platinum, Natural rubber, Sulfur, Acetate, Polyester, Celluloid, Urethane, Polyethylene, Vinyl, Silicon, Teflon

Charging Methods

  • Contact (Conduction): Charge imparted by direct contact.
  • Induction: Bringing a charged object near a neutral one, causing charge separation and flow.

Charging by Induction

Grounding

  • When a charge reservoir receives additional charge.

Multiple Charges and Net Force

  • The net force on a charge is the vector sum of the forces from all other charges.
  • F{net} = F1 + F_2 + …$$
  • Consider the force between charges 2 and 1, and charges 3 and 1.

Electric Field

  • Force radiating from an electrical charge creates a field.
  • The interaction between points is explained by the behavior of each charge.

Field Lines

  • Arrows extend away from positive charges and toward negative charges.
  • Signify direction of force.
  • The number of lines is proportional to the magnitude of the force.

Electric Field Line Patterns

  • Patterns for objects with unequal amounts of charge display the relative strength and direction of the field.

Conceptual Questions

  • Where does "charge" come from?
  • What would happen if there were no charges?
  • Can an object with a charge create a force between other objects?