Solenoid Magnetic Field Calculator

Calculate the magnetic field strength inside a solenoid given the number of turns, current, length, and core permeability.

MAGNETIC FIELD (B)
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In Gauss
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H Field
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Turns Density
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Total Flux
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Solenoid Magnetic Field Basics

Inside a long solenoid, the magnetic field is remarkably uniform and parallel to the axis of the coil. This uniformity makes solenoids ideal for creating controlled magnetic environments in laboratories and industrial equipment. The field outside the solenoid is very weak, essentially zero for an ideal infinite solenoid.

The magnetic field strength depends on the turn density (turns per unit length), the current flowing through the wire, and the permeability of any core material. Ampere's Law provides a straightforward derivation of the field inside the solenoid.

The Formula

B = μ0 · μr · n · I
n = N / L   |   H = n · I   |   B = μH

Magnetic Field Comparison

SourceMagnetic Field
Earth's surface25 - 65 μT
Refrigerator magnet~5 mT
Typical lab solenoid0.01 - 1 T
MRI machine1.5 - 3 T
Superconducting magnetUp to 45 T

Applications

  • MRI machines: Superconducting solenoids generate the strong, uniform fields needed for magnetic resonance imaging.
  • Particle accelerators: Solenoid magnets focus charged particle beams in accelerators and detectors.
  • Electromagnetic valves: Solenoid actuators use the magnetic field to move a plunger, controlling fluid flow.

Frequently Asked Questions

Is the field truly uniform inside a solenoid?

For an ideal infinitely long solenoid, yes. For real solenoids of finite length, the field is approximately uniform in the central region but weakens and diverges near the ends. At the exact center of the end face, the field is about half the value at the center of the solenoid.

How can I increase the magnetic field?

You can increase B by: (1) increasing the current, (2) increasing the number of turns per unit length, or (3) inserting a high-permeability core material such as iron or ferrite. An iron core can increase the field by factors of thousands.

What limits the maximum field in a solenoid?

Practical limits include the current-carrying capacity of the wire (heating from resistance), magnetic saturation of the core material, and mechanical stress from the magnetic forces. Superconducting solenoids overcome the heating limit but face limits from the critical magnetic field of the superconductor.