Charge density higher on sharp ends

[Quantumkid]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

first part can be done by using the fact that electric field outside the sphere is given by E = q / 4(pi)(e_0)r^2
some confusion at second one

 

[SammyS]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

first part can be done by using the fact that electric field outside the sphere is given by E = q / 4(pi)(e_0)r^2
some confusion at second one

You don't know the charge on each sphere, so E = q / (4(π)(ε₀)r²) will not get you anywhere until you do know those relative charge values. (Also, parentheses are important.)

The spheres are connected by a wire so their surfaces are at the same potential. Use that to find the relative charge on the spheres.