PhysSandbox

Electric Dipole Field (2D)

A fixed two-charge dipole on the x-axis uses the Coulomb superposition V = Σ k qᵢ/rᵢ on a regular grid. A masked min/max range colors the heatmap away from singularities; equipotentials come from marching squares on that grid; field lines integrate forward along E from seeds near the positive charge until they reach the negative charge or the boundary.

Who it's for: Introductory electrostatics; complements the free-form Electric Field Visualizer with a formula-forward dipole preset.

Key terms

  • electric dipole
  • equipotential
  • field line
  • Coulomb potential
  • dipole moment

How it works

This page is dedicated to a **pure dipole** in 2D: two point charges **+q** and **−q** on the **x**-axis. The **scalar potential** V adds 1/r contributions; **electric field lines** follow **E** (perpendicular to equipotentials). Compare with the general **Electric Field** lab where you place arbitrary charges.

Key equations

V(r) = Σᵢ k qᵢ / |r − rᵢ|
E = −∇V   (field lines tangent to E)
Far from origin: V ∝ (p·r̂)/r² ,   |p| = 2aq

Frequently asked questions

Why do contours look jagged near the charges?
The potential diverges at point charges; the visualization masks grid points very close to each charge when setting the color scale, and contour segments are piecewise linear on a finite grid.
How does this differ from the general electric field page?
That sandbox lets you place many charges interactively. Here the geometry is locked to a textbook ±q dipole so the text can quote standard dipole-field vocabulary and far-field behavior.

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