HOME / Applications / Understanding Eddy Currents in Conducting Discs: Factors & Analysis

A cylindrical region contains a homogenous, time-varying magnetic field ; B_{0} is the field magnitude and is vertical unit vector. Since there is no electric charge in the system, the changing magnetic field is the sole cause of the electric field . According to Farady's equation :

(eq.1)

or in the case where only has z component:

(eq.2)

where r and represent radial and angular coordinates of the cylindrical coordinate system (Fig. 1).

Due to the symmetry of the problem, its analysis can be simplified by noting that does not depend on , i.e. . Equation 2 therefore, takes the following form:

(eq.3)

**Figure 1 -** a) Copper disc in vertical magnetic field;b) Changing magnetic field is produced inside a cylinder wrapped in coils that carry AC current;

Eddy current distribution in a copper disc can be easily simulated in** EMS** as a **AC Magnetic ** study. To create a uniform magnetic field inside the cylinder, allow a certain thickness to its wall so that you can define the wall as a wound coil. A cylinder with inner radius of 15mm and height of 50mm, should be used to define a **Wound Coil** with 100 turns and **RMS current magnitude per turn** of .For the **Current phase** select 0º - this will produce a cosine current profile in the coil. This current will in turn induce a relatively uniform flux density of magnitude over the volume of the copper disc (radius: 3mm), placed in the center of the cylinder. To help magnetic field align vertically inside the cylinder, add **Normal Flux** boundary conditions to cylinder caps and **Tangential Flux **boundary condition to the inner face of the cylinder wall.

To help the magnetic field align vertically inside the cylinder, Normal Flux boundary condition to cylinder caps and Tangential Flux boundary condition to the inner face of the cylinder wall, should be added.

To do define the Normal Flux,

- In the EMS manger tree right-click on the
**Load/Restraint**folder and select**Normal Flux**. - Click inside the Faces for
**Normal Flux box**then select Cylinder caps . - Click OK .

To do define the Tangential Flux,

- In the EMS manger tree right-click on the
**Load/Restraint**folder and select**Tangential Flux**. - Click inside the Faces for
**Tangential Flux**box then select the inner face of the Cylinder wall . - Click OK .

To show how to define the Wound Coil, see “Force in a magnetic circuit” example.

To set up Eddy Effects, right-click the copper disc in the EMS tree and select Turn on **Eddy Effects** .

To get a high resolution of current density results in the copper disc, a Mesh control of 0.1 mm should be applied to the copper disc.

To do so,

- In the EMS manger tree right-click on the
**Mesh**folder and select**Apply Mesh Control**. - Click inside the
**Bodies**box then select the inner face of the copper disc . - Under Control Parameters click inside the
**Element Size**box and type 0.1 mm. - Click OK .

To mesh the model:

- In the EMS manger tree, right-click on the
**Mesh**icon and select**Create Mesh**. - Click OK .

The application note explores the behavior of eddy currents within a conducting disc under a time-varying magnetic field, providing insights through theoretical analysis and practical simulation. By examining Faraday's law and Ohm's law, it elucidates the mechanisms governing the induction and distribution of eddy currents, emphasizing their dependence on magnetic field properties and material conductivity. Through simulations in EMS, it demonstrates how to model and analyze eddy current phenomena, highlighting the importance of boundary conditions, coil setups, and meshing parameters. The note's findings offer valuable guidance for researchers and engineers seeking to understand and mitigate the effects of eddy currents in various systems, ultimately contributing to improved efficiency and reliability in electromagnetic applications. Overall, this comprehensive exploration advances the understanding and application of eddy current behavior in conducting discs, facilitating future innovations in electromagnetic engineering.

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