Electric Field Lines: Visualizing Coulomb's Law

simulator beginner ~8 min
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Electric dipole — field lines from +1 μC to -1 μC

Two opposite point charges create a dipole electric field. Field lines originate from the positive charge and terminate on the negative charge. The field is strongest between the charges and weakens with distance, following Coulomb's inverse-square law.

Formula

F = kQ₁Q₂/r² (Coulomb's law)
E = kQ/r² (electric field from point charge)
V = kQ/r (electric potential)

Visualizing the Invisible: Electric Field Lines

Electric fields are invisible, but we can map them using field lines — a concept introduced by Michael Faraday in the 1830s. Each line shows the direction a positive test charge would move if placed at that point. The density of lines indicates field strength: closely spaced lines mean a strong field, widely spaced lines mean a weak field.

Coulomb's Law and Point Charges

The electric field around a point charge follows Coulomb's law: E = kQ/r². A single positive charge creates field lines radiating outward in all directions. A single negative charge has lines pointing inward. The inverse-square falloff means the field drops rapidly with distance — doubling the distance reduces the field to one quarter.

Dipoles and Charge Configurations

When two opposite charges are placed near each other, they form a dipole. Field lines curve from the positive charge to the negative charge, creating the characteristic dipole pattern seen in this simulation. Like charges create a repulsive pattern with a neutral point between them where the field is zero. More complex arrangements produce intricate field patterns.

Equipotential Lines and Energy

Perpendicular to the field lines are equipotential lines — contours of constant electric potential. Moving a charge along an equipotential requires no work, just like walking along a contour line on a topographic map. The voltage difference between equipotentials determines the energy gained or lost by a charge moving between them.

FAQ

What are electric field lines?

Electric field lines are imaginary lines that represent the direction and strength of an electric field. They point in the direction a positive test charge would move. Lines originate on positive charges and end on negative charges. Closer spacing means stronger field.

What is Coulomb's law?

Coulomb's law states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance: F = kQ₁Q₂/r², where k = 8.99 × 10⁹ N·m²/C².

What are equipotential lines?

Equipotential lines connect points of equal electric potential. They are always perpendicular to field lines. No work is done moving a charge along an equipotential line. For a point charge, equipotentials are concentric circles.

Why do field lines never cross?

Field lines never cross because the electric field has a unique direction at every point. If lines crossed, there would be two different field directions at the crossing point, which is physically impossible.

Sources

Embed

<iframe src="https://homo-deus.com/lab/electromagnetism/electric-field-lines/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub