Force Between Coil and Core / Electromagnet

Simplified pull-force model

Calculation
Quick Introduction

This calculator uses a simplified air-gap dominated model for electromagnet pull force. Force scales linearly with effective pole area and quadratically with flux density.

The B estimate from \(N\cdot I\) and gap length is a practical approximation for concept design when gap reluctance dominates.

Schema:
1) define geometry (pole area, gap)
2) set turns and current
3) compute B and force, then validate thermally
Formulas (MathJax)
\[F\approx\frac{B^2\,A}{2\mu_0}\]
\[B\approx\mu_0\frac{N\,I}{g}\quad(\text{air-gap dominated})\]
\[I\approx\frac{g}{\mu_0N}\sqrt{\frac{2\mu_0F}{A}}\]
\[A\,[m^2]=A\,[cm^2]\cdot10^{-4},\quad g\,[m]=g\,[mm]\cdot10^{-3}\]
Legend
  • \(F\): pull force [N]
  • \(B\): air-gap flux density [T]
  • \(A\): effective pole area [m²]
  • \(\mu_0\): permeability of free space
  • \(N\): turns
  • \(I\): coil current [A]
  • \(g\): air gap [m]


Examples
At B=0.8T and A=4.5cm², pull force is in the tens of newtons range.
Reducing air gap strongly increases B and therefore force (quadratic B² relationship).
Detailed Documentation & Summary

Electromagnet force estimation is key for contactors, lifting magnets, latches, and valve actuators. This model emphasizes the air-gap as dominant reluctance and enables fast first-order sizing in concept stages.

Practical behavior depends on additional effects: core saturation, fringing at gap edges, nonlinear B-H curves, winding heating, duty cycle, and mechanical tolerances. Therefore results should be validated with measurements or FEM for final design.

Summary
  • Computes force, flux density, or required current
  • Uses air-gap dominated simplified model
  • Suitable for preliminary electromagnet sizing

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