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Solenoid Magnetic Field (Biot-Savart) Calculator

A solenoid is a helical coil of wire that generates a uniform, concentrated magnetic field along its interior axis when energized with electrical current.

Total number of wire loops wrapped around the coil.

Axial length of the wound coil in centimeters.

Direct electrical current flowing through the wire in Amperes.

Core magnetic permeability material (ferromagnetic cores multiply field strength hundreds of times).

Calculated Result
0.013 T

Magnetic Field Strength (B)

Flux Density (Gauss)

125.7 Gauss

Flux Density (Tesla)

0.0126 T

Turn Density

5,000 turns/m

Core Permeability

1×

Calculation Breakdown

  1. Linear Turn Density5,000.0 turns/meter (1000 turns over 20 cm)n=NLn = \frac{N}{L}
  2. Core PermeabilityRelative Permeability \mu_r = 1 (air vacuum)μ=μ0⋅μr\mu = \mu_0 \cdot \mu_r
  3. Axial Magnetic Flux Density (B)0.01257 Tesla (125.66 Gauss)B=μ0μrnIB = \mu_0 \mu_r n I

Magnetic Field vs Current (1000 turns, 20 cm air core)

Interactive visualization based on your current inputs

Field (Gauss)
0.0791572363140.5 A1.0 A2.0 A3.0 A5.0 ACurrent (A)Field (Gauss)

What Is the Solenoid Magnetic Field (Biot-Savart) Calculator?

A solenoid is an electromechanical device consisting of tightly wound helical wire turns that produce a strong magnetic field when energized.

Solenoids are essential in relays, fuel injectors, MRI machines, particle accelerators, and inductor chokes.

How Does the Solenoid Magnetic Field (Biot-Savart) Calculator Work?

Current circulating in each wire loop creates concentric circular magnetic lines of force.

By superposition, interior fields reinforce constructively into a strong, uniform axial vector, while exterior fields cancel.

Solenoid Magnetic Field (Biot-Savart) Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

B=μ0μrNLIB = \mu_0 \mu_r \frac{N}{L} I

Magnetic flux density depends directly on turn density (n = N/L), electrical current (I), and relative magnetic permeability of the core material (μ_r).

How to Use the Solenoid Magnetic Field (Biot-Savart) Calculator

  1. Input the total turn count and physical coil length in centimeters.
  2. Enter the electrical excitation current in Amperes.
  3. Select the core material to factor in magnetic amplification.

Step-by-Step Example Calculation

Air-Core Laboratory Solenoid

Input Values:

turns:1000
length:20
current:2
core:air_vacuum
Worked Steps: A 20 cm solenoid with 1000 turns carrying 2 A in an air core generates a uniform internal magnetic field of 0.0126 Tesla (125.7 Gauss).

Understanding Your Result

Magnetic Field (Tesla & Gauss): Core flux density along the central axis.

Turn Density (turns/m): Number of loops per linear meter.

Factors That Affect the Result

  • Turn Density: Packing more turns into a shorter length boosts field strength linearly.
  • Current: Directly increases magnetic flux density.
  • Core Material: Ferromagnetic cores provide dramatic amplification.

When Should You Use This Calculator?

  • Designing electromechanical solenoid actuators and magnetic valves.
  • Physics laboratory experiments investigating magnetic induction and Faraday’s law.

Assumptions & Limitations

  • Assumes a long solenoid where length is much greater than coil diameter.
  • Neglects ferromagnetic core non-linear saturation effects.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Ampèrian magnetostatic solution with 100% theoretical precision.

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