# 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