Solenoid Magnetic Field Calculator

Solenoid Magnetic Field

A long solenoid creates a nearly uniform magnetic field inside its coils. The field strength depends on current, coil density, and the magnetic properties of the core material.

Magnetic Field Formula

$$B = \mu_0 \mu_r n I, \quad n = \frac{N}{L}$$

$B$ is magnetic flux density in tesla, $\mu_0 = 4\pi \times 10^{-7}$ H/m is the vacuum permeability, $\mu_r$ is relative permeability of the core, $n$ is turns per meter, $N$ is total turns, $L$ is solenoid length in meters, and $I$ is current in amperes.

Example: 500 turns over 0.2 m with 2 A and air core ($\mu_r = 1$) gives $n = 2500$ turns/m and $B \approx 6.28$ mT.

Core Material Effect

Iron or ferrite cores raise $\mu_r$ and amplify the field for the same current. This formula assumes a uniform, long solenoid where end effects are small.

Related tools: LM317 Calculator and Op-Amp Gain Calculator.

Frequently Asked Questions

What is n in the solenoid formula?

n is turns per unit length, $n = N/L$. More turns packed into a shorter length produce a stronger field.

When is the uniform field approximation valid?

It works well when the solenoid is much longer than its diameter and you evaluate the field near the center, away from the open ends.

What is relative permeability?

Relative permeability $\mu_r$ compares a material to vacuum. Air and non-magnetic materials use $\mu_r \approx 1$. Ferromagnetic cores can have much larger values.

What units does B use?

Magnetic flux density $B$ is measured in tesla (T). Small fields are often quoted in millitesla (mT) or microtesla (µT).

Does direction matter?

Yes. Field direction follows the right-hand rule along the coil axis. Magnitude depends on current, turns density, and core permeability.

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Solenoid Magnetic Field Calculator