General Physics 2 (Lesson 4) - Electric Charge, Coulomb's Law, Electric Fields, and Electric Flux

Conductors and Insulators

• Conductivity: Measure of ease at which an electric charge moves.
• Conductors: Materials allowing easy charge flow (e.g., metals).
• Insulators: Materials resisting charge flow (e.g., ceramics).
• Semiconductors: Intermediate conductivity (e.g., resistor, capacitor, diode, transistor).
• Superconductors: Offer almost zero resistance below critical temperatures.
• Charging by Rubbing: Transfer of charge between materials. Triboelectric series helps predict charge.

Coulomb's Law

• Defines electric force $F<em>E$ between two charged particles: $F</em>E = k \frac{|q<em>1q</em>2|}{r^2}$, where:
  • $k$ is Coulomb's constant (approximately $9 × 10^9 N⋅m^2/C^2$)
  • $q<em>1$ and $q</em>2$ are charges in coulombs.
  • $r$ is the distance in meters.
• Similar in form to Newton's law of universal gravitation: $F<em>G = G \frac{m</em>1m_2}{r^2}$
• Superposition Principle: Total force on a charge is the vector sum of individual forces from other charges.

Electric Field

• Electric field intensity is the strength of the electric field at a point.
• Defined as force per unit charge: $E = \frac{F<em>E}{q</em>0}$
• Electric field due to a point charge: $E = k \frac{|q|}{r^2}$
• Units: newton/coulomb (N/C)
• Electric field is a vector quantity and follows the superposition principle.
• Force on a charge in an electric field: $F_E = E|q|$. Direction is opposite for negative charges.

Electric Flux

• Measure of the number of field lines passing through a surface.
• $Φ = E ⋅ A = EA cos θ$, where θ is the angle between the electric field and the area vector.
• Electric flux is a scalar quantity with units of $N⋅m^2/C$.

Gauss's Law

• Total electric flux through a closed surface relates to the enclosed charge:
  $Φ<em>{total} = EA cos θ = \frac{q</em>{total}}{∈<em>0}$ where $∈</em>0$ is the permittivity of free space ($8.8542 × 10^{-12} C^2/N⋅m^2$).
• In integral form: $Φ = ∫E⋅dA$

Charge Distribution

• Gauss's law can be used to compute electric fields for symmetrical charge distributions.
• Linear charge density: $λ$ (charge per unit length).
• Surface charge density: $σ$ (charge per unit area).
• Volume charge density: $ρ$ (charge per unit volume).