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

  • 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