Electric Charges & Fields

Drag two charges and watch the inverse-square force update live, with proper LaTeX formula.

Drag a test charge among 4 fixed charges — net force = vector sum of individual forces.

Radial outward (+) or inward (−) lines with animated dots showing field direction.

Streamlines from + to −. Adjustable separation. Animated dots travel along lines.

Two +, two −, quadrupole, three + — switch and watch the line patterns morph.

1/r² curve with live cursor. Check E falls fourfold when r doubles.

E(z) = kQz/(z²+R²)^(3/2). Maximum at z=R/√2, demonstrated visually.

Radial E field perpendicular to a long charged wire. Falls as 1/r.

Uniform E = σ/2ε₀ — independent of distance from sheet.

Axial E is double the equatorial E at the same r (for a short dipole).

τ = pE sinθ. Drag dipole to rotate, watch torque arrow flip.

Oscillates with ω = √(pE/I). Includes damping for visual realism.

Φ = E·A·cosθ. Tilt the loop and watch flux follow a cosine curve.

Drag a charge in/out of a Gaussian sphere. Φ = Q_enc/ε₀ regardless of position inside.

E = 0 inside a uniformly charged shell, kQ/r² outside. Plot with live cursor.

Closed Gaussian cylinder around a line charge. E = λ/(2πε₀r).

Electrons drift to surface; E inside drops to zero in equilibrium.

Toggle the cage on/off — see how a closed conductor shields its interior.

σ ∝ 1/R_curvature — sharp regions concentrate charge and produce strongest fields.

Same potential ⇒ Q ∝ R, σ ∝ 1/R. Smaller sphere has higher field.