Magnetic Field of a Straight Current-Carrying Wire Calculator

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Dominik Czernia, PhD

Dominik Czernia

PhD, Institute of Nuclear Physics PAN

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Research Gate

Dominik Czernia, PhD, is a physicist at the Institute of Nuclear Physics in Kraków, specializing in condensed matter physics with a focus on molecular magnetism. He has led several national research projects, pioneering innovative approaches to novel materials for high technology. Passionate about making science accessible, Dominik has created various calculators, mostly in physics and math categories. In his free time, he enjoys family walks, city explorations, mountain hiking, and traveling everywhere by bike. See full profile

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Bogna Szyk and Adena Benn

Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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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!