A highly charged piece of metal with uniform potential throu

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 Times 10^6 [V/m]. What is the maximum possible potential of a metal sphere of 0.1mm radius? There isn\'t enough information to determine the answer. 100V 300V

Solution

Electric field at surface of sphere = kq/r^2

and maximum field can be 3 x 10^6 V/m .

3 x 10^6 = 9 x 10^9 x q / (0.1 x 10^-3)^2

q = 3.33 x 10^-12 C

so Maximum potential = kq/r

= (9 x 10^9 x 3.33 x 10^-12)/(0.1 x 10^-3)
= 300 volt .......Ans