An isolated metal sphere is to be used to store charge at high potential. The charge stored may be assumed to be a point charge at the centre of the sphere. The sphere has a radius of 
. Electrical breakdown (a spark) occurs in the air surrounding the sphere when the electric field strength at the surface of the sphere exceeds 
.
Show that the maximum charge that can be stored on the sphere is 
.
Calculate the potential of the sphere for this maximum charge.
.
