Faraday Law of Induction

\(U_{ind}=N\cdot\frac{d\Phi}{dt}\) – voltage from changing magnetic flux

Calculation
Quick Introduction

Faraday's law states that a changing magnetic flux through a coil induces an electrical voltage. Higher turns count and faster flux variation increase induced voltage.

This calculator is useful for quick predesign in sensors, generators, transformers, and general induction concepts.

Sizing schema:
1) define coil turns N
2) estimate flux dynamics dΦ/dt
3) verify Uind and iterate N or flux profile
Formulas (MathJax)
\[U_{ind}=N\cdot\frac{d\Phi}{dt}\]
\[\frac{d\Phi}{dt}=\frac{U_{ind}}{N}\]
\[N=\frac{U_{ind}}{d\Phi/dt}\]
\[\Phi=B\cdot A\quad\Rightarrow\quad\frac{d\Phi}{dt}=A\cdot\frac{dB}{dt}\;(A\;constant)\]
Symbol Legend
  • \(U_{ind}\): induced voltage [V]
  • \(N\): number of turns [-]
  • \(\Phi\): magnetic flux [Wb]
  • \(d\Phi/dt\): flux change rate [Wb/s]
  • \(B\): flux density [T], \(A\): area [m²]


Examples
Example 1: \(N=250\), \(d\Phi/dt=0.048\,Wb/s\) ⇒ \(U_{ind}=12\,V\).
Example 2: \(U_{ind}=5\,V\), \(N=100\) ⇒ \(d\Phi/dt=0.05\,Wb/s\).
Example 3: \(U_{ind}=24\,V\), \(d\Phi/dt=0.08\,Wb/s\) ⇒ \(N=300\).
Detailed Documentation & Summary

Faraday's induction law is one of the core equations in electrical engineering. It links time-varying magnetic flux with a measurable electrical voltage. In practical systems, flux variation can be caused by moving magnets, alternating currents in nearby windings, or controlled magnetic field changes in cores.

For engineering estimates, magnitude-only calculations are often sufficient, as in this calculator. For full physical interpretation, sign and polarity follow Lenz's law (opposition to cause). Real-world design also requires considering winding resistance, leakage inductance, core losses, saturation behavior, and frequency-dependent effects.

Typical use cases include transformers, generators, inductive sensing, power converter magnetics, wireless power transfer, and EMC analysis of fast magnetic transients. This tool helps decide whether a target voltage should be achieved by increasing turns count or by increasing flux-change dynamics.

Summary
  • Calculates Uind, dΦ/dt, or N in three modes
  • Supports quick predesign of coil and induction applications
  • Highlights direct trade-off between turns count and magnetic dynamics

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