To calculate the eddy current loss density in a transformer core, you can use the following formula:
Eddy Current Loss Density (P_e) = K_e * B^2 * f^2 * t^2
Where:
P_e is the eddy current loss density (power per unit volume) in Watts per cubic meter (W/m^3).
K_e is a constant that depends on the material properties and the geometry of the core.
B is the maximum magnetic flux density in Tesla (T).
f is the frequency of the alternating current in Hertz (Hz).
t is the thickness of the laminations in meters (m).
Please note that this formula assumes that the core is made up of laminations to reduce eddy current losses. The laminations are thin insulated sheets stacked together, which helps to minimize the circulating current paths and hence, the eddy current losses.
It's essential to use appropriate units for all variables to get the result in the desired unit, such as W/m^3. Also, keep in mind that this formula is a simplified model and may not account for all factors affecting eddy current losses, but it provides a good approximation for most practical applications. If you need more accurate results, advanced simulations or measurements might be necessary.