AP Physics 2: Advanced Concepts & Calculations

Front

Define Electric Potential (V) physically and mathematically relative to a point charge.

Back

Electric potential V is the work done per unit charge to bring a small positive test charge from infinity to a specific point in the field against the electric force. For a point charge Q, V = kQ/r. Unlike electric field (a vector), V is a scalar field. Superposition applies algebraically: V_total = sum(kQ_i/r_i).

Front

Equipotential Lines vs. Electric Field Lines relationship.

Back

Equipotential lines connect points of equal electric potential. Key relationships: 1) Electric field lines are always perpendicular to equipotential lines. 2) No work is required to move a charge along an equipotential surface (W = qΔV = 0). 3) In regions of strong electric fields, equipotential lines are packed closely together.

Front

Derivation of the Capacitance for a Parallel Plate Capacitor.

Back

C = Q/ΔV. Using Gauss's Law, E = σ/ε₀ = Q/(Aε₀). Since E is uniform, ΔV = Ed = Qd/(Aε₀). Substituting ΔV into C = Q/ΔV gives C = Q / (Qd/Aε₀) = ε₀A/d. Capacitance depends only on geometry (Area A, distance d) and dielectric constant (ε), NOT on voltage or charge.

Front

Dielectric Constant (κ) effect on Capacitor properties (C, V, Q, E).

Back

Inserting a dielectric material reduces the internal electric field (E = E₀/κ) and potential difference (ΔV = ΔV₀/κ) due to polarization of the material. Capacitance increases by factor κ: C = κC₀. If the capacitor is isolated (charge Q constant), voltage drops. If connected to a battery (V constant), charge stored increases by factor κ.

Front

Internal Resistance (r) and Terminal Voltage in a Real Battery.

Back

Real batteries have internal resistance r. Terminal Voltage V_term = ε - Ir, where ε is emf and I is current. As current (load) increases, the voltage drop across the internal resistor (Ir) increases, decreasing the usable terminal voltage. If the circuit is open (I=0), V_term equals ε.