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.

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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Key equations

Frequently asked questions

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Frequently asked questions