# A Conducting Disc

A conducting disc is given a charge Q. As the disc is conducting it must be equipotential and hence the charge distribution will not be uniform. From what I know the charge will have a tendency to spread out more towards the rim and will arrange itself such that the net field is perpendicular everywhere on the surface of the disc. Is it possible to find this charge distribution and the electric field produced by it ? If so then how ?

Find $$E$$ field of a ring of charge $$Q$$ on an axis perpendicular to the center of the ring.
Then use the solution of the ring to find the $$E$$ field for the disk by integrating the ring solution over the area of the disk.
The charge density on the disk will be $$\sigma = \frac{Q}{2\pi r^2}$$ where $$r$$ is the radius of the disk. Again, ignore the edge effects.