PhL Physics Library

Eddy Current

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Eddy currents—also called Foucault currents—is a fundamental example of electromagnetic induction occurring inside bulk conductive materials. When we analyze them carefully, we see that these localized circulating currents arise directly from the principles embodied in Faraday’s Law and Lenz’s Law. In this article, we shall view their origin through those laws and understand how changing magnetic flux induces internal current loops within the conductor. We will also work through how the associated power dissipation can be derived mathematically and then reflect on what that means physically—particularly in terms of magnetic damping and resistive heating. As we shall see, these effects are not merely theoretical curiosities but have significant practical consequences in modern electromechanical systems.

Introduction

When a solid conductor is placed in a non-uniform or time-varying magnetic field, it’s noticable that it doesn’t simply remain unaffected. What actually happens is far more interesting: the changing magnetic flux induces internal loops of electric current within the material itself. And unlike the familiar currents that are neatly confined to a conducting wire, these so-called “eddies” are not restricted to a single path. Instead, they swirl throughout the volume of the conductor, forming closed loops in planes perpendicular to the magnetic flux, giving rise to what we call eddy currents.

 

Let me remind you that this phenomenon was first carefully observed by Léon Foucault in 1855 and it arises directly from the fundamental interplay between moving charges and magnetic fields. Now, although we often treat eddy currents as an undesirable or parasitic loss—especially in transformer cores—you should not think of them as merely wasteful effects. In fact, the very same currents form the functional backbone of important modern technologies, from electromagnetic braking systems to everyday induction cooking devices.

The Physics of Induction

The emergence of eddy currents is governed by **Faraday’s Law of Induction**, which states that a change in magnetic flux ($\Phi_B$) through a circuit induces an electromotive force (EMF). In a bulk conductor, this EMF ($\mathcal{E}$) drives a current density ($J$) determined by the material’s conductivity ($\sigma$).

According to **Lenz’s Law**, the direction of these induced currents is such that the magnetic field they create opposes the change in the original magnetic field. This creates a mechanical “drag” or “magnetic damping” effect when a conductor moves through a field.

Central Mathematical Expression

The power loss ($P$) per unit mass due to eddy currents in a thin sheet or lamination—a critical value for engineers trying to minimize energy waste—is expressed by the following equation:

$$P = \frac{\pi^2 B_p^2 f^2 d^2}{6 \rho D}$$

Where:

* $B_p$ is the peak magnetic field (T).
* $f$ is the frequency of the magnetic field variations (Hz).
* $d$ is the thickness of the sheet (m).
* $\rho$ is the resistivity of the material ($\Omega \cdot m$).
* $D$ is the density of the material ($kg/m^3$).

This expression highlights that power loss is proportional to the square of the thickness, which is why transformer cores are constructed from thin, insulated laminations rather than solid blocks of iron.

Electrodynamic Consequences

The behavior of eddy currents is highly sensitive to the geometry and material properties of the conductor. In high-frequency applications, a phenomenon known as the **skin effect** occurs, where the eddy currents circulate primarily near the surface, effectively increasing the material’s resistance.

In practical application, these currents are utilized in :-

  1. Electromagnetic Braking : Where the kinetic energy of a moving vehicle is converted into heat via eddy currents induced in a spinning disc.
  2. Induction Heating : Where high-frequency magnetic fields generate intense eddy currents to melt metals with high precision.
  3. Metal Detection : Where the secondary magnetic field produced by eddy currents in a buried object is sensed by a receiver coil.

Conclusion

Eddy currents are a sophisticated reminder that electromagnetism is rarely a “neat” affair confined to wires. They represent a complex transformation of energy—shifting from magnetic flux to kinetic current and, eventually, to thermal energy. While they pose significant challenges in power distribution due to resistive heating, their mastery has enabled the development of frictionless braking systems and high-efficiency heating technologies. Understanding the square-law relationship between frequency, thickness, and power loss remains a cornerstone of electromagnetic design and material science.


Eddy currents, also known as Foucault currents, represent a fundamental manifestation of electromagnetic induction within bulk conductive media. This article examines the genesis of these localized circulating currents through the lens of Faraday’s Law and Lenz’s Law. We explore the mathematical derivation of power dissipation associated with these currents and discuss the practical implications of magnetic damping and resistive heating in modern electromechanical systems.

Introduction

When a solid conductor is subjected to a non-uniform or time-varying magnetic field, it does not merely sit idle. Instead, the changing magnetic flux induces internal loops of electric current. Unlike currents confined to a wire, these “eddies” swirl within the volume of the material in planes perpendicular to the magnetic flux.

First observed in detail by Léon Foucault in 1855, the phenomenon is a direct consequence of the interplay between moving charges and magnetic fields. While often viewed as a parasitic loss in transformer cores, eddy currents are the functional backbone of technologies ranging from electromagnetic braking to induction cooking.

The Physics of Induction

The emergence of eddy currents is governed by **Faraday’s Law of Induction**, which states that a change in magnetic flux ($\Phi_B$) through a circuit induces an electromotive force (EMF). In a bulk conductor, this EMF ($\mathcal{E}$) drives a current density ($J$) determined by the material’s conductivity ($\sigma$).

According to **Lenz’s Law**, the direction of these induced currents is such that the magnetic field they create opposes the change in the original magnetic field. This creates a mechanical “drag” or “magnetic damping” effect when a conductor moves through a field.

Central Mathematical Expression

The power loss ($P$) per unit mass due to eddy currents in a thin sheet or lamination—a critical value for engineers trying to minimize energy waste—is expressed by the following equation:

$$P = \frac{\pi^2 B_p^2 f^2 d^2}{6 \rho D}$$

Where:

* $B_p$ is the peak magnetic field (T).
* $f$ is the frequency of the magnetic field variations (Hz).
* $d$ is the thickness of the sheet (m).
* $\rho$ is the resistivity of the material ($\Omega \cdot m$).
* $D$ is the density of the material ($kg/m^3$).

This expression highlights that power loss is proportional to the square of the thickness, which is why transformer cores are constructed from thin, insulated laminations rather than solid blocks of iron.

Electrodynamic Consequences

The behavior of eddy currents is highly sensitive to the geometry and material properties of the conductor. In high-frequency applications, a phenomenon known as the **skin effect** occurs, where the eddy currents circulate primarily near the surface, effectively increasing the material’s resistance.

In practical application, these currents are utilized in :-

  1. Electromagnetic Braking : Where the kinetic energy of a moving vehicle is converted into heat via eddy currents induced in a spinning disc.
  2. Induction Heating : Where high-frequency magnetic fields generate intense eddy currents to melt metals with high precision.
  3. Metal Detection : Where the secondary magnetic field produced by eddy currents in a buried object is sensed by a receiver coil.

Conclusion

Eddy currents are a sophisticated reminder that electromagnetism is rarely a “neat” affair confined to wires. They represent a complex transformation of energy—shifting from magnetic flux to kinetic current and, eventually, to thermal energy. While they pose significant challenges in power distribution due to resistive heating, their mastery has enabled the development of frictionless braking systems and high-efficiency heating technologies. Understanding the square-law relationship between frequency, thickness, and power loss remains a cornerstone of electromagnetic design and material science.