# Solenoid Magnetic Field Calculator

Created by Miłosz Panfil, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jan 23, 2023

The solenoid magnetic field calculator helps you compute the magnetic field inside a long solenoid. Curious to see what a solenoid is and how to calculate the magnetic field of a solenoid? Just continue reading. You will also learn about the solenoid magnetic field equation.

## What is a solenoid?

If we run a current through a wire, there is a magnetic field around it. A solenoid is a wire wound tightly in a long, thin coil. Due to its shape, if we run current through the solenoid, there will be a strong magnetic field inside of it and little magnetic field outside of it.

Solenoids are used in many practical applications whenever there is a need to create a magnetic field. Unlike magnets, we can control the strength of the magnetic field by just adjusting the electric current. Solenoids, and in general coils, are also basic inductive elements in electric circuits. To find out more, check out our solenoid inductance calculator, RLC circuit calculator, and inductive reactance calculator.

## Solenoid magnetic field equation

A solenoid of infinite length is the easiest to describe. The magnetic field of an infinite solenoid is precisely zero outside and has a constant value inside the solenoid. The infinite solenoid is often a reasonable approximation of a real-world, finite-length solenoid if we can accept that the magnetic field will be slightly different from that of an infinite solenoid in the vicinity of the ends.

The magnetic field inside a long solenoid is properly calculated by using the cross product (see the cross product calculator) and maybe the right-hand rule, but all that can be simplified into:

$B = \frac{\mu_0NI}{L}$

where:

• $B$ – Magnetic field;
• $\mu_0 = 1.25664 \times 10^{-6}\ \rm T\cdot m/A$ is the vacuum permeability;
• $N$ – Number of turns in the solenoid;
• $I$ – Electric current; and
• $L$ is the length of the solenoid.

## How to calculate magnetic field of a solenoid?

The simplest way to calculate the magnetic field of a solenoid is to use our calculator. Simply specify:

• Number of turns;
• The electric current; and
• The length of the solenoid.

This will return the magnetic field inside of it. To learn about the effect of the magnetic field on charged particles, try our Lorentz force calculator.

## FAQ

### What is the origin of the magnetic field in a solenoid?

The magnetic field in a solenoid originates from the current flowing in the coiling of the solenoid itself. As the magnetic field propagates radially from the wire, we can identify two regions:

• One inside the solenoid, where the direction of the field generated at two diametrically opposite side of the coil aligns, generating a stronger, almost uniform magnetic field; and
• One outside, where the directions of the magnetic fields generated by the elements are precisely opposite, canceling the magnetic field. Outside of a solenoid, the magnetic field is exactly 0.

### How do I calculate the magnetic field inside a solenoid?

To calculate the magnetic field inside a solenoid:

1. Measure the current in the wire, I;
2. Count the number of complete coilings in the solenoid, N;
3. Measure the length of the device, L.
4. Calculate the strength of the magnetic field:
B = µ0 · N · I/L

where µ0 is the magnetic permeability of the vacuum.

### How do I calculate the magnetic field outside a solenoid?

The magnetic field outside a solenoid is zero: the fields generated by each coiling on the diametrally opposed points of a spire cancel each other on the outside of the solenoid, causing the field to go to zero. Only at the terminations of the component can you observe a non-zero field on the outside of the coil.

### What is B in a solenoid with 100 turns in 10 cm, and current 0.1 A?

The field is 125 mT. To calculate the magnetic field inside this solenoid, simply apply the formula:
B = µ0 · N · I/L,
And substitute the following values:

• N = 100;
• L = 0.1 m; and
• I = 0.1 A.

The result is: B = 1.25664E-6 T ⋅ m/A · 100 · 0.1 A/0.1 m =1.25E-4 T

Miłosz Panfil, PhD
Current
A
Length
m
Number of turns
Magnetic Field
T
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