Electrostatic Potential & Capacitance
18 topics · 18 interactive simulations
Potential due to Point Charge
V = kq/r. Drag a probe and read live potential with full heatmap.
V & E vs Distance
1/r and 1/r² overlaid — confirm E = −dV/dr.
Equipotential Surfaces
Banded contours for single charge, dipole, two-+. Always perpendicular to E.
E = −dV/dx
Linear V → constant E. Graphs side-by-side.
Potential of Dipole
V = (kp cosθ)/r². Zero on equatorial plane, max on axis.
Work Moving a Charge
W = q(V_B − V_A). Independent of path between two equipotentials.
Parallel-Plate Capacitor
C = ε₀A/d. Animated dots show field. Live Q, E, U.
Effect of Dielectric
C' = κC₀. Toggle V-fixed (Q grows) vs Q-fixed (V drops).
Energy Stored in Capacitor
U = ½CV². Visualized as triangular area under Q-V curve.
RC Charging
q(t) = CV(1 − e^(−t/τ)). Watch the curve build with τ marked.
RC Discharging
q(t) = Q₀ e^(−t/τ). 37% remaining at τ marked clearly.
Capacitors in Series
1/C_eq = Σ 1/Cᵢ. Same Q. Voltage divides inversely with C.
Capacitors in Parallel
C_eq = ΣCᵢ. Same V. Charge splits proportionally to C.
Variable (Air-Gang) Capacitor
C ∝ |cosθ|. Rotate the shaft to tune from radio receiver-style sweep.
Dielectric Slab Insertion
Slab gets pulled in by force F = ε₀bV²(κ−1)/(2d).
Force Between Plates
F = Q²/(2ε₀A). Always attractive (opposite sign plates).
Dielectric Breakdown
Each dielectric has a breakdown E_max. Above it, the dielectric arcs.
Battery Removal Case
Insert dielectric with battery on/off — different physics. Compare side-by-side.