Unit 3: Electric Force, Field, and Potential

Concepts

Protons and electrons - At an atomic level, all charge comes from protons and electrons. Protons and electrons have multiple properties, for example:

• All protons are identical to each other in size, mass and charge, and all electrons are identical to each other in size, mass, and charge.
• The charges of protons and electrons are equal but opposite.
• Both protons and electrons have the same elementary charge, which is 1.6 x 10^-19C (coulombs).
• At its base state, an atom has an equal number of protons and electrons, which gives it a net charge of zero. For an atom to gain a positive charge and become a cation, electrons must be removed. For an atom to gain a negative charge and become an ion, electrons must be added.
• Electrons can move freely from one object to another while protons can't, so a change in charge always depends on electrons moving.
• Like charges repel, while opposite charges attract.

Conservation of charge - Net electric charge cannot be created nor destroyed. This also means that whenever charge is transferred between objects, the net charge produced will always be zero.

Insulators and conductors - Insulators are substances which slow down the flow of electrons, while conductors are substances that allow electrons to flow much more freely.

Charging - How objects gain or lose electrons. Methods of charging include:

• Charging by friction - Works primarily with insulators. Happens by rubbing two objects together, which dislodges electrons and causes them to move from one object to another.
• Charging by conduction - Works best with conductors. Happens by touching two objects together, which causes electrons to move from one object to another.
• Charging by induction - Works best with conductors. Happens when two grounded objects have their charges separated and are then separated themselves.
• Grounding - When a conductor is attached to a much bigger object with much more charge. This leads to any excess electrons in the conductor going to the larger object.

Electric fields - Electric fields are created by charges and extend throughout space to create electrostatic forces on other charges.

Electric field lines - Used to represent electric fields graphically. The closer the lines are to each other, the stronger the field is at that point.

Electric potential - The electric potential energy divided by unit charge. Also referred to as voltage. Electric potential is a scalar, which means direction doesn't matter when adding potential fromm multiple charges up, only sign.

Isolines - Used to represent electric potential graphically. These lines are always perpendicular to electric field lines. The lines themselves represent the amount of potential, while the space between them represents how quickly the potential is changing between points (closer lines = quicker change).

Coulomb's law constant - 1/4πε_o or 9 x 10⁹ (N⋅m²)/C².

Formulas

F_e = k(q₁q₂)/r² - Used to find the force between two charges. Electric force = (Coulomb's law constant)((magnitude of charge 1)(magnitude of charge 2))/(distance between charges)².

E = F_e/q - Used to find the strength of an electric field and its direction due to a point charge. Vector of the electric field = vector of the force experienced by a test charge / the magnitude of the test charge.

E = k(Q/r²) - Used to find the magnitude of an electric field at a point. Electric field = (Coulomb's constant)(magnitude of charge/(distance from the point to the charge)².

V = PE_e/q - Used to find electric potential. Electric potential = (electric potential energy)/magnitude of charge).

E = V/d - Used to find the magnitude of the electric field in capacitors. Electric field = change in electric potential / distance between parallel plates.

V = k(Q/r) - Used to find electric potential due to a point charge at some distance. Electric potential = (Coulomb's constant)(magnitude of point charge/distance from point charge).