Field of a long straight wire

Intermediate

Circles around the wire.

Key relationB = μ₀I/2πr

B = μ₀I/(2πr), with circular field lines around the wire in the direction of the right-hand grip rule.

Worked example

10 A at 5 cm: 40 μT.

Common mistake

Falls as 1/r.

In more detail

The field of a long straight wire carrying current I is B = μ0I/(2πr), circling the wire. It falls off as 1/r with distance from the wire.

Power lines produce magnetic fields that can be measured nearby.
Wire-based sensors use this field to detect current.
Engineers designing a power line estimate the magnetic field around the wire to judge exposure to nearby homes.

Which way does the field circle?

Use the right-hand grip rule: thumb along the current, fingers curl in the field direction.

Does the field fall off as 1/r?

Yes, for an infinitely long straight wire.

Does the field get weaker with distance?

Yes. The field falls off as one over the distance from the wire, so it weakens gradually.