Tell me whether I solved this electrostatics problem correctly

[thequirk]

Here's the problem:

The passage of a thundercloud overhead caused the vertical electric field strength in the atmosphere, measured at the ground, to rise to 0.1 statvolt/cm [E_0].

(a) How much charge didthe thundercloud contain, in esu per cm^2 of horizontal area?
(b) Suppose there was enough water in the thundercloud in the form of 1-millimeter-diameter [convert to cm and divide by two, call this r] drops to make 0.25 cm of rainfall [d], and that it was those drops which carried the charge. How large was the electric field strength at the surface of one of those drops?

Here's what I got:

(a) E_0 = 2πσ, from which we get σ = E_0/(2π)
(b) Here's where I am not sure whether I am doing the right thing or not.

Consider some part of the water at the ground of area A at the top (assuming level water).

Φ = 4πq and Φ = E_0 * A => q = AE_0/(4π)
This is the total charge there is.

On the other hand,
Adρ = AE_0/(4π) <=> ρ = E_0/(4πd)

Then the charge which is carried by one drop is:
Q = (4/3)πρr^3 => Q = (r^3)E_0/(3d)

Since the field at the surface is Q/R^2, we get:

E = R*E_0/(3d)

 

[lippyka]

Where R = 2r.Therefore, the electric field strength at the surface of one of those drops is:E = 4r*E_0/(3d)

 

[m2003]

Your solution appears to be correct. Good job! You used the correct equations and correctly applied them to solve the problem. Your explanation is also clear and easy to follow. Keep up the good work!