Magnetic Field of a Straight Wire Calculator
Find the magnetic field around a straight current-carrying wire.
Current in a wire wraps a circular magnetic field around it.
How the Math Works
The magnetic field B around a straight current-carrying wire is calculated using the formula B = μ₀·I ÷ (2π·r), where μ₀ is the permeability of free space (a constant equal to 4π × 10⁻⁷ T·m/A), I is the current in amperes, and r is the perpendicular distance from the wire in meters. This equation shows that the magnetic field strength is directly proportional to the current and inversely proportional to the distance from the wire, meaning doubling the current doubles the field strength, while doubling the distance halves it. The formula derives from Ampère's Law, which relates magnetic fields to the currents that produce them, and is valid for infinitely long, straight wires in a vacuum or air.
Practical Applications
This calculation is essential in electrical engineering for designing power transmission lines, motors, transformers, and electronic circuits. Engineers use it to ensure magnetic fields remain within safe limits around high-voltage cables, prevent interference with sensitive equipment, or determine the necessary spacing between current-carrying conductors. Researchers also apply it in electromagnetism experiments or to model magnetic effects in materials. By quantifying the field strength, professionals can optimize device efficiency, avoid electromagnetic compatibility issues, and ensure compliance with safety regulations in industrial and consumer electronics.
Day-to-Day Use
Understanding this formula helps explain the invisible magnetic fields surrounding power lines, household appliances, and electronic devices. It aids in designing safer electrical systems, such as ensuring power cables in buildings don't generate excessive magnetic fields that could affect medical devices or human health. The principles also underpin technologies like electric guitars (which use magnetic pickups), speakers, and MRI machines, where controlled magnetic fields are critical. Additionally, it informs everyday decisions, like why high-voltage power lines are placed away from schools or how magnetic shielding in appliances protects internal components from external interference.
Worked example
10 A at 5 cm → about 4 × 10⁻⁵ T.
FAQ
Which way does the field point?
Around the wire, given by the right-hand rule.