What is an electric field?

An electric field is a region of space around a charged particle or object where other charged particles experience a force. The field is a vector quantity — at every point in space it has both a magnitude and a direction. Positive charges create fields that radiate outward, while negative charges create fields that point inward.

How does Coulomb's law work?

Coulomb's law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is F = k·q₁·q₂/r², where k ≈ 8.99 × 10⁹ N·m²/C² is Coulomb's constant. Like charges repel and opposite charges attract.

What are electric field lines?

Electric field lines are imaginary curves used to visualize the direction and strength of an electric field. They originate on positive charges and terminate on negative charges. The density of field lines indicates field strength — closer lines mean a stronger field. Field lines never cross each other.

What are equipotential lines?

Equipotential lines connect points in space that have the same electric potential (voltage). They are always perpendicular to electric field lines. No work is done when moving a charge along an equipotential surface. Around a point charge, equipotential lines form concentric circles.

Home▸Electromagnetism▸Electric Field Visualizer - Interactive Coulomb's Law and Electrostatics

🧪 Electric Field Visualizer - Interactive Coulomb's Law and Electrostatics

Visualise electric fields and equipotential surfaces for point charges and dipoles in real time. Explore Coulomb's law, superposition of fields, and Gauss's law - perfect for GCSE and A-level electrostatics.

Electromagnetism2DModerate60 FPS

The Physics of Electric Fields

⚡ Coulomb's Law and the Inverse Square

Every charged object creates an electric field in the space around it. The force between two point charges is given by Coulomb's law: F = kq&sub1q&sub2/r², where k = 8.99×10&sup9 N·m²/C². This is structurally identical to Newton's law of gravitation — both are inverse-square force laws. Key differences: electric forces can be repulsive (like charges), and electric forces are typically 10³&sup6 times stronger than gravity between two protons.

📈 Superposition Principle

When multiple charges are present, the total electric field at any point is the vector sum of the fields from each individual charge: E⃗_total = E⃗₁ + E⃗₂ + .... This simulator calculates the field from all charges simultaneously, visualised as field lines and vector arrows. The linearity of the superposition principle is a direct consequence of Maxwell's equations being linear PDEs.

🌹 Electric Field Lines

Field lines show the direction a positive test charge would accelerate. They obey strict rules: they start on positive charges (sources) and end on negative charges (sinks). Line density indicates field strength — closely packed lines mean a stronger field. Lines never cross (that would imply two forces at the same point). Near a positive charge the field is radially outward; near a negative charge, radially inward.

⚛️ Equipotentials and Electric Potential

Equipotential surfaces are regions where electric potential V is constant. They are always perpendicular to field lines. Moving a charge along an equipotential requires no work (W = qΔV = 0). Around a single point charge, equipotentials are concentric spheres (circles in 2D). For a dipole, they form complex oval shapes. Capacitors store energy in the potential difference between parallel equipotential plates.

Key Equations

Quantity	Symbol	Formula	Notes
Coulomb force	F	kq&sub1q&sub2/r²	k = 8.99×10&sup9 N·m²/C² (Coulomb's constant)
Electric field	E	F/q = kQ/r²	Force per unit positive test charge
Electric potential	V	kQ/r	Energy per unit charge; scalar
Potential energy	U	kq&sub1q&sub2/r	Positive for like charges (repulsive)
Work done	W	qΔV = q(V_B−V_A)	Zero along equipotential surfaces
Gauss's law	Φ_E	&oiintE·dA = Q_enc/ɛ&sub0	Total flux through closed surface = enclosed charge / ɛ&sub0
Dipole moment	p	qd	Points from − to + charge; d = separation
Field of dipole	E_axial	~1/r³	Falls off faster than single charge (1/r²)

Curriculum Links

Level	Topic	Concepts Covered
GCSE Physics	Electricity	Static charge; attraction/repulsion; electric current basics
A-Level Physics	Fields (Topic 5/6)	Coulomb's law; field strength E = F/q; potential V = kQ/r; field lines; equipotentials; capacitance
IB Physics HL	Electric & Magnetic Fields (Topic 5/10)	Coulomb's law; superposition; electric potential; capacitance; Gauss's law (HL)
AP Physics C: E&M	Electrostatics	Coulomb's law; Gauss's law; conductor/insulator behaviour; potential energy
University Year 1	Electromagnetism	Vector fields; Gauss's law in integral form; capacitors; dielectric polarisation
University Year 2+	Classical Electrodynamics	Maxwell's equations; multipole expansions; Green's functions; boundary conditions

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⚙ Under the hood

This simulation demonstrates Coulomb’s law and electrostatic principles through an interactive visualization of electric fields. Users can manipulate charges to observe the resulting field patterns.

Coulomb's LawElectrostatics

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install