Electrostatic Potential & Capacitance

V = kq/r. Drag a probe and read live potential with full heatmap.

1/r and 1/r² overlaid — confirm E = −dV/dr.

Banded contours for single charge, dipole, two-+. Always perpendicular to E.

Linear V → constant E. Graphs side-by-side.

V = (kp cosθ)/r². Zero on equatorial plane, max on axis.

W = q(V_B − V_A). Independent of path between two equipotentials.

C = ε₀A/d. Animated dots show field. Live Q, E, U.

C' = κC₀. Toggle V-fixed (Q grows) vs Q-fixed (V drops).

U = ½CV². Visualized as triangular area under Q-V curve.

q(t) = CV(1 − e^(−t/τ)). Watch the curve build with τ marked.

q(t) = Q₀ e^(−t/τ). 37% remaining at τ marked clearly.

1/C_eq = Σ 1/Cᵢ. Same Q. Voltage divides inversely with C.

C_eq = ΣCᵢ. Same V. Charge splits proportionally to C.

C ∝ |cosθ|. Rotate the shaft to tune from radio receiver-style sweep.

Slab gets pulled in by force F = ε₀bV²(κ−1)/(2d).

F = Q²/(2ε₀A). Always attractive (opposite sign plates).

Each dielectric has a breakdown E_max. Above it, the dielectric arcs.

Insert dielectric with battery on/off — different physics. Compare side-by-side.