Uppose that a metal file cabinet is charged. How does the charge concentration at the corners of the cabinet compare with the charge concentration on the flat parts of the cabinet

The charge is greater at the corners  of the cabinet comparing with the charge concentration on the flat parts of the cabinet

Metals becomes positively charged when they loose electrons. This is in contrast with the non metals where they gain electrons to be a negatively charged one. The carrier of charges in metals are the electrons present in it. The valence electrons that are present in the atoms of metallic structure can be able to move freely and forms a Fermi gas.

Fermi gas refers to the clouding of free electrons. The charges gets distributed uniformly except the edges. In the example given, in a charged metal file cabinet the charges are distributed uniformly all over except the corners. There will be larger concentration of changes that exists in corners of the metal file cabinet.

there is an explationation of this on a site called crash   course world history 1