Question

A charged conical conductor loses it's charge earlier than a similarly charged sphere. Why?

Answer 1

charges location inside a conductor depends upon its shape. Due to conical shape, a large amount of charge is present near to point shape than at the base. So amount of work done (voltage) reguired to drain out all charges is much less than a similarly charged sphere which has charges spread out uniformly across the sphere

Answer 2

This Phenomenon is considered as the the "corona discharge".