Electric Field
Place positive and negative charges to visualize electric field lines and vectors. Explore Coulomb's law and the superposition principle in real-time.
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&sub1;q&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: E⃗total = 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&sub1;q&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&sub1;q&sub2;/r | Positive for like charges (repulsive) |
| Work done | W | qΔV = q(VB−VA) | Zero along equipotential surfaces |
| Gauss's law | ΦE | &oiint;E·dA = Qenc/ɛ&sub0; | Total flux through closed surface = enclosed charge / ɛ&sub0; |
| Dipole moment | p | qd | Points from − to + charge; d = separation |
| Field of dipole | Eaxial | ~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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