Rucete ✏ AP Physics 2 In a Nutshell
1. Electric Fields and Potentials
This chapter introduces the nature of electric charges, Coulomb’s law, electric fields, electric potential, and capacitance. It covers the behavior of charges, how electric forces are measured, and the ways energy is stored and transferred in electric fields.
The Nature of Electric Charges
• Electric charge arises from the transfer of electrons; protons are positive, electrons are negative.
• Like charges repel, opposite charges attract.
• Static electricity results from localized electron transfer (e.g., rubbing ebonite with cloth).
• Ions in solution and electrodes demonstrate charge transfer behavior in liquids.
• Conservation of charge: total electric charge remains constant during transfer.
The Detection and Measurement of Electric Charges
• Insulators (e.g., rubber, plastic) hold static charge; conductors (e.g., metals) allow charges to flow freely.
• Grounding a conductor removes excess charge.
• Pith balls detect presence of charge qualitatively.
• Electroscopes qualitatively measure charge by leaf divergence.
• Charging by friction, contact, and induction are key methods to transfer charge.
Coulomb’s Law
• Electrostatic force between two point charges: F = k·(q₁q₂)/r²
• k ≈ 9 × 10⁹ N·m²/C²; force acts along the line joining charges.
• Inverse-square law, similar to gravitational force.
• Force can be attractive or repulsive depending on signs of charges.
• Superposition principle: net force is the vector sum of all individual forces.
The Electric Field
• A charge creates an electric field E around it, influencing other charges nearby.
• Field strength: E = F/q
• Units: N/C (newtons per coulomb).
• Field direction is the direction of force on a positive test charge.
• Field lines radiate outward from positive charges and inward toward negative charges.
• Field strength decreases with distance (1/r² relationship).
Electric Potential
• Electric potential (V) is electric potential energy per unit charge: V = U/q
• Units: volts (V); 1 V = 1 J/C.
• Potential difference (ΔV) between two points = work done per unit charge to move between them.
• Uniform electric fields (like between parallel plates): E = ΔV/d
• Positive charges move naturally toward lower potential; negative charges move toward higher potential.
Equipotential Lines
• Equipotential surfaces connect points with the same electric potential.
• No work is done moving along an equipotential surface.
• Equipotentials are always perpendicular to electric field lines.
• Around a point charge, equipotential surfaces are concentric spheres.
Capacitance and Energy Storage
• Capacitors store electric potential energy by separating charges.
• Capacitance (C): C = q/V
• Units: farads (F); 1 F = 1 C/V.
• Parallel-plate capacitor: C = ε₀A/d, where A is plate area, d is separation, ε₀ ≈ 8.85 × 10⁻¹² C²/N·m².
Energy Stored in a Capacitor
• Energy (U) = ½CV² = ½q²/C = ½qV
• Larger capacitance or voltage means more stored energy.
In a Nutshell
Electric charges interact through forces and fields, following Coulomb’s law. Electric fields describe the influence of charges, while electric potential describes energy per charge. Capacitors store energy by maintaining electric potential differences, and understanding fields, potentials, and energy transfer is key to analyzing electric systems.