# Charge density of turning object

A charged disk or sphere will create currents around its turning axis if a rotation is added. The total current can then be calculated by adding all concentric currents together. Every current (I take the example of a thin charged disk, as it is the most easiest casus) is as big as:

$$dI = dQ / dt = f*\sigma*2 \pi *rdr$$

So the total charge would be something like:

$$I = \omega\int_0^R \sigma r dr$$

With $R$ the radius of the disk,$f$ the frequency, $\omega$ the angular speed (so we can leave the $2\pi$ out) and $\sigma$ the charge density.

In my physics book they consider $\sigma$ as a constant. But I was wondering: as electrons (who determine the charge) have mass, they also have a centrifugal force, which would imply that the charge density is NOT the same at every distance from the centre, so we would have to define a $\sigma$ in function of $r$ (so $\sigma$ is not just total charge on total surface).

Would this centrifugal force give considerable different results and if so, could anyone show me a calculation of the difference in total current? Also if the difference is not considerable for a small disk, would it be for a very large disk, because the centrifugal force is bigger at a bigger radius (for example a disk with radius 1000km)?