Magnetic Field Induced by a Current-Carrying Wire

Amperian loop radius (meters)

0.001

current (amperes)

0.001

wire radius (meters)

1

height of Amperian loop (meters)

5

opacity

0.75

B = 2.×

-13

10

Teslas

An infinitely long uniform wire carrying current induces a magnetic field (more precisely, magnetic induction)

B

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

∮B·dℓ=

μ

0

I

enc

and can be solved for

B

to get

B=

μ

0

I

enc

2πa

, where

μ

0

is the vacuum permeability constant,

I

enc

is the current enclosed by the Amperian loop, and

a

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).