# Help Understanding Equation for Characteristic Time of Induced Magnetic Field

I am reading this book, the part in particular about Eddy-current separation starting at Page 246, in it there is an equation for calculating the "characteristic time with which the induced magnetic field decays in the particle".

$$\tau = \mu_0\sigma_psb^2$$

Where:

• $\mu_0$ is the permeability of free space
• $\sigma_p$ is the specific electric conductivity of a particle [S/m]
• $s$ is the shape factor of the particle
• $b$ is the particle radius

I am hoping someone can reflect some light on what $s$ is and how to calculate it, "shape factor" isn't very descriptive and I cannot find anywhere in the book describing it in further detail.

This shape factor is also used in the force equations that I am intersted in...

Another part of the equation I am unclear on is $b$, what if the particle is a cube or cuboid, what should the radius be then?

• After reading through several papers it appears $b$ is the largest diameter that would fit in the projected shape. I am still unsure about $s$, from what I have read perhaps it is likening the shape to a sphere or cylinder. – Lerp Dec 16 '13 at 15:02