Electrostatics: Charge, Induction, and Conductors — Quick Reference

Fundamentals of Electric Charge

  • Charge is a fundamental property of matter; positive (protons) and negative (electrons)
  • Atoms are neutral when #protons = #electrons
  • Charge is quantized: charges come in integer multiples of the elementary charge ee
  • Elementary charge: e≈1.6×10−19 Ce \approx 1.6 \times 10^{-19} \text{ C}
  • Common submultiples: 1 nC=10−9 C1 \text{ nC} = 10^{-9} \text{ C}
  • Net charge cannot be created or destroyed; it can be transferred between objects (conservation of charge)

How Charges Interact

  • Like charges repel; opposite charges attract
  • Forces are vector and follow Newton's third law: equal and opposite
  • Force magnitude increases with charge magnitude

Charge Quantities and Calculation

  • Fundamental relation: q=neq = n e
  • If electrons are transferred, sign is negative (electrons carry negative charge)
  • Example value: for electrons transferred, Q=neQ = n e with e≈1.6×10−19 Ce \approx 1.6 \times 10^{-19} \text{ C}

Methods of Charging

  • Friction (triboelectric): transfer of electrons by rubbing materials
    • Example: balloon on hair becomes negatively charged
  • Conduction (contact): charge flows when objects touch; conductors share charge
  • Induction (near-field, no contact): charge separation (polarization) in a neutral object due to an external charge

Grounding and Induction

  • Grounding = connect to Earth (a huge reservoir); allows excess charge to flow away or be supplied
  • Induction steps (no contact):
    • Bring a charged rod near a neutral conductor (no contact)
    • Charges rearrange: opposite charges attract toward the rod, like charges repel away
    • Ground the conductor to allow excess charge to flow to Earth
    • Remove ground; the conductor retains a net charge on removal
  • Net charge is not created by induction; only separated/polarized during the process

Static Electricity and Electrostatics

  • Static electricity: buildup of electric charges due to transfer of electrons with no continuous current
  • Electrostatics: study of stationary charges and their fields

Materials and Devices

  • Conductors: allow free charge flow (e.g., metals like copper, silver)
  • Insulators: resist charge flow (e.g., glass, rubber)
  • Electroscope: device to observe charging by conduction or induction

Quick Numerical Reference

  • If n electrons are transferred: Q=neQ = n e
  • For n=8.2×109n = 8.2 \times 10^{9} electrons, Q≈(8.2×109)×(1.6×10−19)≈1.31×10−9 C=1.31 nCQ \approx (8.2 \times 10^{9}) \times (1.6 \times 10^{-19}) \approx 1.31 \times 10^{-9} \text{ C} = 1.31 \text{ nC}
  • Sign is negative for electrons

Quick Summary Formulas

  • q=neq = n e
  • e≈1.6×10−19 Ce \approx 1.6 \times 10^{-19} \text{ C}
  • 1 nC=10−9 C1 \text{ nC} = 10^{-9} \text{ C}