A highly charged piece of metal (with uniform potential throughout) tends to spark at places where the radius of curvature is small, or at places where there are sharp points. The breakdown electric field strength for air is about 3 106 V/m.
(a) It is possible to calculate the maximum possible potential (relative to infinity) in air of a metal sphere of 15 cm radius. First, what is the maximum charge you can put on this sphere?
C
For that amount of charge, what is the potential of the sphere relative to infinity?
volts
(b) Next, calculate the maximum possible potential relative to infinity in air of a metal sphere of only 0.2 mm radius. What is the maximum charge you can put on this sphere?
C
For that amount of charge, what is the potential of the sphere relative to infinity?
volts