Coulomb's Law & Ampère's Law

Coulomb's Law & Ampère's Law Visually

Explore Coulomb's Law and Ampère's Law through interactive simulations. Understand electric and magnetic forces, inverse square laws, and electromagnetic field interactions with real-world examples and visualizations.

Coulomb's Law & Ampère's Law Point Charges Force / Field Calculation Field Lines Visualization Electric / Magnetic Interaction Law Verification Visual Simulation

What are Coulomb's Law and Ampère's Law?

Coulomb's Law and Ampère's Law are two fundamental principles in electromagnetism that describe the forces between electric charges and the relationship between electric currents and magnetic fields, respectively.

Coulomb's Law quantifies the electrostatic force between two point charges, stating that the force is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Coulomb's Law

The fundamental law of electrostatics

Mathematical Expression

Coulomb's Law describes the electrostatic force between two point charges:

F = ke × (q1 × q2) / r2

Where:

  • F = Electrostatic force between charges (Newtons)
  • ke = Coulomb's constant (8.988 × 109 N⋅m2/C2)
  • q1, q2 = Magnitudes of the charges (Coulombs)
  • r = Distance between the charges (meters)

Key Principles

  • Force is directly proportional to the product of charges
  • Force is inversely proportional to the square of distance
  • Likes charges repel, opposite charges attract
  • Acts along the line joining the charges
  • Inverse square law (similar to gravity)

Interactive Coulomb's Law Simulation

Force Magnitude: 898.8 N

Ampère's Law

The fundamental law of magnetostatics

Mathematical Expression

Ampère's Law relates the magnetic field around a closed loop to the electric current passing through it:

∮ B ⋅ dl = μ0 × Ienc

Where:

  • ∮ B ⋅ dl = Line integral of magnetic field around closed loop
  • μ0 = Permeability of free space (4π × 10-7 T⋅m/A)
  • Ienc = Total current enclosed by the loop

Key Principles

  • Relates magnetic fields to electric currents
  • Valid for steady currents only
  • Symmetric current distributions simplify calculations
  • Integral form of one of Maxwell's equations
  • Differential form: ∇ × B = μ₀J

Interactive Ampère's Law Simulation

Magnetic Field: 6.28×10⁻⁶ T

3D Electromagnetic Field Visualization

Explore electric and magnetic fields in three dimensions

3D Electromagnetic Field Simulator

Real-World Applications

How Coulomb's Law and Ampère's Law impact our daily lives

Electronics

Coulomb's Law explains how electronic components like capacitors store charge, while Ampère's Law governs the behavior of inductors and transformers.

Power Systems

Ampère's Law is essential for designing electrical generators, motors, and power transmission systems that form the backbone of modern civilization.

Wireless Communication

Both laws are fundamental to understanding how antennas transmit and receive electromagnetic waves for radio, TV, WiFi, and cellular communications.

Calculation Tools

Coulomb's Law Calculator
Force: 0 N

Calculation Tools

Ampère's Law Calculator
Magnetic Field: 0 T

Comparison with Related Physics Fields

Understanding how electromagnetism differs from other branches of physics

Electromagnetism vs. Classical Mechanics

Aspect Classical Mechanics Electromagnetism
Force Type Contact & Gravitational Electric & Magnetic
Range Finite (contact) or Infinite (gravity) Infinite
Inverse Square Law Gravity only Electric forces
Field Concept Not fundamental Fundamental concept

Electromagnetism vs. Quantum Mechanics

Aspect Classical Electromagnetism Quantum Electrodynamics
Description Continuous fields Discrete photons
Uncertainty Deterministic Probabilistic
Scale Macroscopic Atomic/Subatomic
Mathematical Framework Vector calculus Quantum field theory

Key Distinctions

Infinite Range

Unlike contact forces in mechanics, electromagnetic forces act at infinite distances, though they weaken with distance.

Field Mediation

Electromagnetic forces are mediated by fields that exist in the space between charges, unlike direct contact forces.

Wave Propagation

Changing electric and magnetic fields propagate as waves, enabling wireless communication across vast distances.

Data Management

Export and import your simulation data

Simulation Data Management

Save your simulation configurations and results for future reference or sharing with colleagues.