Formula & Calculator
Ampere's Law
Relates the circulating magnetic field around a closed loop to the current passing through it.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| B | Magnetic flux density | T |
| μ₀ | Permeability of free space (4π×10⁻⁷) | H/m |
| I_enc | Enclosed electric current | A |
| N | Number of turns (for solenoids/toroids) | dimensionless |
| r | Radius of Amperian loop (wire/toroid) | m |
| L | Length of solenoid | m |
What it means
Ampere’s law states that the line integral of the magnetic field B around a closed path is equal to μ₀ times the total current enclosed by the path. Mathematically, ∮ B·dl = μ₀·I_enc. It is one of Maxwell’s equations and is the magnetic counterpart of Gauss’s law for electricity. Ampere’s law is used to calculate magnetic fields for symmetric current distributions, such as those from long straight wires, solenoids, and toroids. For a long straight wire carrying current I, the magnetic field at distance r is B = μ₀I/(2πr). This law is fundamental in electromagnetism and is used in the design of magnetic circuits, transformers, and inductors. Example: For a long straight wire with I=10A, the magnetic field at r=0.1m is B = (4π×10⁻⁷ * 10) / (2π * 0.1) = (4π×10⁻⁶)/(0.2π) = 2×10⁻⁵ T (20 µT).
Worked example
Ampere's Law – Practical Example
Real‑World| Parameter | Value |
|---|---|
| I | 10 A |
| r | 0.1 m |
| μ₀ | 4π×10⁻⁷ H/m |
| Formula | B = (μ₀·I) / (2π·r) |
Common mistakes
- Closed loop: The line integral is around a closed path.
- Current enclosed: Only currents passing through the surface bounded by the loop.
- Sign: Use the right‑hand rule for current direction relative to the loop.
- Displacement current: For time‑varying fields, add displacement current term (Maxwell’s correction).
- Magnetic permeability μ₀: For media, use μ.
Applications
Ampere's law relates the circulation of the magnetic field around a closed loop to the enclosed current, forming the basis for magnetostatics. Engineers use it to design electromagnets, motors, and inductors, calculating the field produced by current‑carrying conductors. It is also used to analyse the magnetic field of transmission lines and to design magnetic shielding. By applying Ampere's law, professionals can determine the field distribution in symmetric geometries, essential for magnetic circuit design. This law is one of Maxwell's equations and is fundamental to electrical engineering.
- Design of electromagnets and magnetic actuators
- Motor and transformer magnetic circuit analysis
- Transmission line magnetic field assessment
- Magnetic shielding and EMC design
- Educational foundation of magnetic fields