Electric Charges & Fields
20 topics · 20 interactive simulations
Coulomb's Law
Drag two charges and watch the inverse-square force update live, with proper LaTeX formula.
Superposition of Forces
Drag a test charge among 4 fixed charges — net force = vector sum of individual forces.
Field Lines — Single Charge
Radial outward (+) or inward (−) lines with animated dots showing field direction.
Field Lines — Dipole
Streamlines from + to −. Adjustable separation. Animated dots travel along lines.
Field Lines — Multiple Charges
Two +, two −, quadrupole, three + — switch and watch the line patterns morph.
E vs r Curve
1/r² curve with live cursor. Check E falls fourfold when r doubles.
Field on Axis of Ring
E(z) = kQz/(z²+R²)^(3/2). Maximum at z=R/√2, demonstrated visually.
Infinite Line Charge
Radial E field perpendicular to a long charged wire. Falls as 1/r.
Infinite Plane Sheet
Uniform E = σ/2ε₀ — independent of distance from sheet.
Dipole — Axial vs Equatorial
Axial E is double the equatorial E at the same r (for a short dipole).
Torque on Dipole
τ = pE sinθ. Drag dipole to rotate, watch torque arrow flip.
Dipole SHM in Uniform Field
Oscillates with ω = √(pE/I). Includes damping for visual realism.
Electric Flux Through Surface
Φ = E·A·cosθ. Tilt the loop and watch flux follow a cosine curve.
Gauss's Law
Drag a charge in/out of a Gaussian sphere. Φ = Q_enc/ε₀ regardless of position inside.
Gaussian Surface — Sphere
E = 0 inside a uniformly charged shell, kQ/r² outside. Plot with live cursor.
Gaussian Surface — Cylinder
Closed Gaussian cylinder around a line charge. E = λ/(2πε₀r).
Field Inside a Conductor
Electrons drift to surface; E inside drops to zero in equilibrium.
Faraday Cage Shielding
Toggle the cage on/off — see how a closed conductor shields its interior.
E vs Conductor Shape
σ ∝ 1/R_curvature — sharp regions concentrate charge and produce strongest fields.
Charge on Connected Spheres
Same potential ⇒ Q ∝ R, σ ∝ 1/R. Smaller sphere has higher field.