Chapter 3 - Electric Force, Field, and Potential

Electric Charge

  • Units of charge: Coulombs (C)   * One proton has a charge of 1.6 x 10^-19 C   * One electron has a charge of -1.6 x 10^-19
  • When an object has more protons than electrons, it’s positively charged
  • When an object has more electrons than protons, it’s negatively charged
  • Like charges repel and opposite charges attract
  • __Quanta__ = the smallest package of a proton or electron that charge comes in
  • Atomic Structure   * Atoms have protons (and neutrons) in the middle and electrons zipping around outside   * Electrons are easier to remove and in static electricity, we assume only electrons are being removed/added
  • __Law of conservation of charge__ - The initial charge of the system will always equal the final charge of the system
  • Conductors vs insulators   * Generally, metals are good conductors and nonmetals are insulators   * __Conductors__ - allow charge to move easily through them   * __Insulators__ - don’t allow charge to move easily through them (held in place)
  • There are 3 ways to charge an object:   * Charging by Friction - rubbing two objects like a fuzzy towel and iron rod results in electrons jumping from one object to the other     * Remember that net charge of the towel-rod system is still the same   * Charging by Contact or Conduction     * When a charged object comes in contact with a neutrally charged object, the electrons disperse so that both objects have the same charge sign       * Bigger objects end up with more charge because they have more room     * Insulators don’t allow as much charge to disperse through contact as conductors do   * Induced Charge, Polarization, and Induction     * Induced charge - a neutrally charged object becomes polarized (electrons clump up on one side of the object and positive charges pile on the other side)     * In AP Physics 2 questions, a grounding wire is often included       * The grounding wire essentially serves as an escape route for charges to escape from the polarized object
  • Charge Distribution   * On conductors, excess charges are pushed to the outside of the object to get away from each other   * On insulators, excess charges stay where they are and don’t disperse

Electric Fields

  • __Field:__ a property of a region that can apply force to objects found in that space
  • Electric fields affect charged particles only   * Charged particles in electric fields experience an electric force

     Field diagram where X is a negative charge and Y is a positive charge

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  • Electric fields are drawn as arrows because they’re vectors   * The longer the arrows, the greater the magnitude of the electric field
  • Units of electric fields: N/C (Newtons/Coulomb)
  • F = qE   * F: electric force   * q: charge   * E: electric field
  • The direction of the force on a positive charge is the same direction as the electric field   * The direction of the force on a negative charge is the opposite direction as the electric field   * Typically, when using the equation F = qE, we solve for the magnitude and find the direction of the electric force and/or field afterward

Electric Potential

  • __Electric potential__: Electric potential energy per unit charge (provided by an electric field)   * Units: 1 V = 1 J/C   * Electric potential is scalar (only have magnitudes)   * “Zero of electric potential” = “ground” = a theoretical distance at which two charged particles are infinitely far away from each other and therefore don’t affect each other   * ==ΔU = qΔV==     * ΔU = difference in electric potential energy     * q = charge     * ΔV = difference in electric potential
  • __Equipotential lines__: Lines on which a charged particle would have the same potential

   Equipotential Diagram

  \   * Equipotential lines are drawn perpendicular to the electric field lines   * It takes energy to move a charge to another equipotential line   * Positive charges are naturally pulled to areas of negative potential   * Negative charges are naturally pulled to areas of positive potential   * Remember that energy is conserved so U + K is constant     * U is electric potential energy and K is kinetic energy

Electrostatics

  • Parallel Plates   * There are 2 metal plates that are parallel - one is positively charged and the other is negatively charged     * This creates a uniform electric field with the arrows pointing from the positive plate to the negative plate   * ==E = ΔV/Δr==     * E = the magnitude of the electric field     * ΔV = the magnitude of the voltage difference between plates     * Δr = the distance between plates   * Parallel plates can be used to make capacitors (a device that stores charges and will be further explored in circuits)     * ==ΔV = Q/C==       * ΔV = the voltage across plates       * Q = charge on each plate       * C = the capacitance of the capacitor     * ==C = kεA/d==       * C = capacitance       * k = dielectric constant - shows how good of an insulator you have between plates       * ε = “vacuum permittivity” = 8.85 x 10^-12 C/Vm
  • Point charges   * ==E = q/(4πεr) = kq/r==     * k = Coulomb’s Law Constant = 9 x 10^9 Nm^2/C^2   * The electric field produced by a positive charge points away from the charge   * The electric field produced by negative charge points toward the charge   * ==V = kq/r==   * ==F = kqq/r^2==     * Where the two q’s are the charges of two point charges     * k = Coulomb’s Law Constant     * r = the distance between the two point charges
  • Electric Field around a point charge or conducting sphere   * ==E = kq/r^2==     * To solve for the magnitude of the electric field     * Inside a conducting sphere, the electric field is 0       * Net force on any charge inside a conducting sphere is 0

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