Solenoid Magnetic Field Calculator

Use Solenoid magnetic field calculator to calculate solenoid magnetic field based on axis using permiability of vaccum,number of turns,current,x-angle and y-angle.

Solenoid Magnetic Field Calculator
Permeability Of Vacuum
Number Of Turns
Current
X-Angle
Y-Angle
Magnetic Field Of Straight Solenoid Based On Axis: {{magneticFieldOfSolenoidBasedOnAxis()}}

How to use Solenoid Magnetic Field Calculator?

Step 1 - Enter the Permeability Of Vacuum

Step 2 - Enter the Number Of Turns

Step 3 - Enter the Current

Step 4 - Enter the X-Angle

Step 5 - Enter the Y-Angle

Step 6 - Calculate Solenoid Magnetic Field

Solenoid Magnetic Field Calculator Formula:

Baxis = ((μ0nI)/2) * (cos(x)-cos(y))

Where,

Baxis = Magnetic Field Of Straight Solenoid Based On Axis

μo = Permeability Of Vacuum

n = Number Of Turns

I = Current

x = Angle

y = Angle

Frequently Asked Questions

What is a solenoid and how does it produce a magnetic field?

A solenoid is a helical coil of wire that produces a nearly uniform magnetic field when electric current flows through it. The magnetic field strength depends on the number of turns, current magnitude, and solenoid geometry. Solenoids are used in relays, electromagnets, inductors, and magnetic shielding applications. The field at any point along the axis is determined by superposing the contributions from each turn.

How does the number of turns affect magnetic field strength?

The magnetic field at the solenoid axis is directly proportional to the number of turns (N) and the current (I). Doubling the turns doubles the field strength, making tightly wound coils essential for applications requiring strong magnetic fields. This linear relationship is fundamental to electromagnet design and transformer operation.

When should I use this solenoid calculation versus Ampere’s Law?

Use this calculator for quick estimation of axial magnetic field in long, straight solenoids with uniform winding. Ampere’s Law provides exact results but requires integration over the entire geometry. This calculator is ideal for design and preliminary analysis, while detailed 3D field mapping requires full electromagnetic simulation or Ampere’s Law integration.

What are the assumptions for solenoid magnetic field calculations?

The calculation assumes the solenoid is infinitely long (or long compared to diameter), windings are tightly spaced, and the field point is far from the ends. Real solenoids have fringe effects at the ends, and fields outside are negligible but nonzero. The formula is most accurate for the central region away from ends.

Solenoid inductance is proportional to the magnetic field strength, which increases with turns squared and decreases with cross-sectional area. The magnetic energy stored in a solenoid equals ½LI². Understanding the field-current relationship is essential for calculating inductance, transformer coupling, and energy in electromagnetic devices.

Physical Basis & References

This calculator applies Ampere’s Law and the Biot-Savart Law for solenoid geometry:

$$B_{axis} = \frac{\mu_0 n I}{2}[\cos(\theta_1) - \cos(\theta_2)]$$

Where angles are measured from the observation point to the solenoid ends.

Key Physics Principles:

  • Ampere’s Law - Relationship between current and magnetic field circulation
  • Biot-Savart Law - Exact calculation of magnetic field from current distributions
  • Superposition - Total field is sum of contributions from all current elements
  • Magnetic field geometry - Field strength depends on angle and relative position

Key Assumptions:

  • Uniform current distribution in windings
  • Tightly spaced turns (continuous approximation)
  • Cylindrical solenoid geometry
  • Observation point on the solenoid axis
  • Far-field region relative to wire diameter

Typical Range of Values:

  • Number of turns: 10 to 10,000 turns
  • Current: 0.1A to 100A
  • Magnetic field: 0.01 mT to 10 T (depending on solenoid size)
  • Field angles: 0° to 180° (fully wound solenoid)

Further Reading:

  • Griffiths, D.J. (2013). Introduction to Electrodynamics, 4th Edition. Pearson.
  • Jackson, J.D. (1998). Classical Electromagnetism, 3rd Edition. Wiley.
  • Hyperphysics: Solenoid Field Theory - Georgia State University

Conclusion

You can read more about Magnetic dipole Moment Magnetic Field Calculator based on Radius using below link

Read more about other Physics Calculator on below links