# Magnetic Field of a Straight Current-Carrying Wire Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Sep 26, 2023

This magnetic field of straight current-carrying wire calculator makes it easy to describe the magnetic field produced by a long, straight current-carrying wire. Read on to understand the basics of this phenomenon and find out how you can estimate the strength of this field.

Be sure to check our electromagnetic force on current-carrying wire and the magnetic force between wires calculators too!

## Magnetic field of a wire

Did you know that electricity is always strictly linked to magnetism? It results from one of Maxwell's equations, which says that a flowing electric current produces a magnetic field. Let us consider the case of a long straight wire which carries an electric current. In this particular situation, magnetic field lines form concentric circles around the cable, and the strength of the magnetic field depends on the distance from the wire and the current flowing through it.

We can also wind a wire tightly in a thin coil, forming a solenoid. To learn more about solenoids, try our solenoids magnetic field calculator.

## How to calculate magnetic field around a wire?

To correctly calculate the magnetic field around a wire, we would need to make use of cross product and the right-hand rule. But we can also approximate. Assuming that our wire is straight and very long, we can estimate a magnetic field around the wire with the following equation:

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

where:

• $I$ — Current flowing through the wire;
• $d$ — Distance from the wire;
• $B$ — Strength of the magnetic field produced at distance $d$;
• $μ_0$ is the permeability of free space, which has the constant value of $\small μ_0 = 4π \times 10^{-7} \rm T \cdot m / A$ (2019 definition).

You can see that the higher the current flowing through the wire and the closer we are to the wire, the stronger the magnetic field produced is.

## Earth's magnetic field

The Earth, other planets, and stars in our universe act like giant magnets. The Earth's magnetic field originates in its core, where very hot electrically conducting fluids are. The motion of these fluids generates a flowing current, just like in the wire, which is then responsible for producing the magnetic field. The mean magnitude of Earth's magnetic field has changed over the years, but presently, it equals about 5 × 10-5 T. Although this is a tiny field, we can still see it on the compass.

Let's use our calculator to estimate a current that must flow in a straight wire to obtain Earth's magnetic field at a distance of 1 cm from the wire. It seems after calculations that we need only 2.5 A to keep up with Earth's magnetic field!

Dominik Czernia, PhD
Current
A
Distance
in
Magnetic field
T
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