Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.

Explanation

With arbitrary q and Q fro A and B respectively.
`E_(A)/E_(B)=((1)/(4pi epsi_(0)) q/a^(2))/((1)/(4pi epsi_(0)) Q/b^(2))=q/Q . b^(2)/a^(2)`
For equilaterial condition, `V_(A)=V_(B)`
`q/(4pi epsi_(0) a)=(Q)/(4pi epsi_(0)b) therefore q/Q=q/b " "E_(A)/E_(B)=a/b. b^(2)/a^(2)=b/a`
`E=sigma/(epsi_(0))`. For pointed ends `sigma=q/A`. As `A to 0` E becomes extremely large. Flat means `A to oo` hence.