# Solenoid Magnetic Field Calculator

Created by Luciano Mino
Last updated: Jun 24, 2022

The solenoid magnetic field calculator can help you find the magnetic field inside a solenoid from its length, number of turns, and current circulating through it.

Ever wondered what is the strength of the magnetic field at the center of a solenoid? In this short article, we will explain the magnetic field of a solenoid equation and pair it with some examples for you to easily comprehend this subject.

## Magnetic field of a solenoid formula. Magnetic field of an infinite solenoid approximation.

A solenoid is simply a wire wrapped around several loops. When a current circulates through this wire, it creates a magnetic field B in its interior.

🙋 If you don't know anything about electricity and its concepts, the is the perfect place to start!

If the solenoid's length is much greater than its radius, we can assume the magnetic field within it to be uniform and try to find the magnetic field of an infinite solenoid.

That way, by using Ampere's law, we can get to the magnetic field of a solenoid equation:

$B = \frac{\mu I N}{L}$

where:

• $I$ is the intensity of the current;
• $N$ is the total number of turns;
• $L$ is the total length of the solenoid; and
• $\mu$ is the permeability of the material inside the solenoid (or permeability of free space).

We can also replace this by the following formula if we know the number of turns per meter $n$ but not the distance:

$B = \mu I n$

This is everything you need to know to start using the solenoid magnetic field calculator! As you can see, finding the magnetic field at the center of a solenoid is pretty straightforward.

💡 The solenoid magnetic field calculator also allows you to change the material inside the solenoid. Simply input the material's permeability and start testing with it!

## Using the solenoid magnetic field calculator

Let's suppose we wanted to find the magnetic field inside a $0.3\ \text{m}$, $200$ turns solenoid, which carries a $2\ \text{A}$ current.

As you can see, the calculator has multiple inputs/outputs (it will also find any missing parameters). Let's go through each one:

• Current. The intensity of the current in amperes. In this example $2\ \text{A}$.
• Length. The solenoid's total length in meters. Here, $0.3\ \text{m}$.
• Number of turns. $200$.
• Permeability (μ). Since, in this case, the solenoid is empty, we use permeability of vacuum, which is exactly $0,0000012566\ \text{H/m}$.
• Magnetic field inside the solenoid. The calculator will use the magnetic field of a solenoid equation to give you the result! In this case, $0.0016755\ \text{T}$
Luciano Mino
Permeability (μ)
H/m
Current
A
Length
m
Number of turns
Magnetic Field
T
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