AP Physics C: E&M Unit 9 Cheatsheet: Electric Potential

Electric potential energy is the work required by an external force to bring charged objects from infinity to their current positions.

Two-point-charge system:

• k = Coulomb constant
• r = separation distance
• Positive when charges repel (same sign)
• Negative when charges attract (opposite sign)

Multi-charge systems: Sum potential energies of all pairwise interactions.

Potential difference between two points:

Change in potential energy:

• If a positive charge moves to lower electric potential, ΔU = qΔV < 0, so the system loses electric potential energy.
• If a positive charge moves to higher electric potential, ΔU_E is positive (the system gains electric potential energy).

Conservation of energy: If only conservative (e.g., electrostatic) forces do work, mechanical energy is conserved and ΔK = -ΔU = -qΔV; if an external agent or nonconservative force also acts, include its work: W_ext = ΔK + ΔU.

When comparing two configurations:

• Same charge, different r: V ∝ 1/r; smaller r → larger |V|
• Same r, different q: V ∝ q; double charge → double potential
• Field vs. potential: E ∝ 1/r²; V ∝ 1/r (different dependencies)

Multi-charge systems:

• Potentials add as scalars (easier than vector addition of fields)
• Opposite charges can cancel V at a point even if E ≠ 0
• Same charges: V always has same sign

Equipotential spacing:

• Closer spacing near strong sources (small r)
• Wider spacing far from sources (large r)