Magnetic Field Calculator

When electric current flows through a straight conductor, it generates a magnetic field in the surrounding space. The magnitude of this field at a perpendicular distance r from an infinitely long straight wire carrying current I is given by:

$$B = \frac{\mu_0 I}{2\pi r}$$

This result comes from applying Ampère's circuital law along a circular Amperian loop of radius r centered on the wire. The enclosed current is I, and by symmetry the field has constant magnitude along the loop, giving $$\oint \vec{B} \cdot d\vec{l} = B(2\pi r) = \mu_0 I$$.

The direction of the field follows the right-hand rule: if the thumb of your right hand points in the direction of current flow, your fingers curl in the direction of the magnetic field lines. The field lines form closed circles around the wire, and the field magnitude falls off as 1/r.

Key properties of this field:

• The field is directly proportional to the current — doubling the current doubles the field strength.
• The field is inversely proportional to the distance — at twice the distance, the field is half as strong.
• The constant $$\mu_0 = 4\pi \times 10^{-7}\,\text{T·m/A}$$ sets the scale in SI units.
• For a finite-length wire, the formula must be modified using the Biot-Savart law with angular limits.

Common unit conversions: 1 T = 10,000 G (gauss), 1 T = 1,000 mT. Earth's magnetic field is roughly 25–65 μT (0.25–0.65 G).

The calculated magnetic field B represents the field strength at the specified distance from the wire. Compare your result with common reference values: Earth's field is about 50 μT, a refrigerator magnet produces ~5 mT, and an MRI machine operates at 1.5–3 T. If the field exceeds safety thresholds for nearby electronics or biological exposure, consider increasing the distance or reducing the current.