# Magnetic Field Induced by a Current-Carrying Wire

Magnetic Field Induced by a Current-Carrying Wire

An infinitely long uniform wire carrying current induces a magnetic field (more precisely, magnetic induction) that varies with the distance from the wire and the amount of current. Ampère's law is used to determine the magnetic field at any point on the imaginary Amperian loop at a given distance from the wire with a given amount of current. Ampère's law is and can be solved for to get , where is the vacuum permeability constant, is the current enclosed by the Amperian loop, and is the radius of the Amperian loop. This Demonstration lets you vary the relative height of the Amperian loop, the Amperian loop radius, current, wire radius, and opacity of the wire to see each variable's effect on the strength of the induced magnetic field, measured in teslas (T).

B

∮B·dℓ=

μ

0

I

enc

B

B=

μ

0

I

enc

2πa

μ

0

I

enc

a