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

• 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 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