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