- #1

doktorwho

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## Homework Statement

A metal ball of radius ##a## is at a distance ##h>>a## from a very long conducting non-charged horizontal metal surface. Calculate the maximum electrical force on a ball under the condition that ##E_{cr}## the critical electric field of air is not breached.

## Homework Equations

3. The Attempt at a Solution [/B]

I applied the mirror theorem and placed a ball of charge ##-Q## on the other end, ##2h## distance away from the first.

##F_2=Q_1E_2## this is the force on ball 1 from ball 2. When ##E=E_{crit}##, we have a maximum charge of ball 1 and ball 2 because they are the same. so we would have ##F_{max}=Q_{max}E_{crit}## and since they are the same ##Q_{max}=E_{crit}16\pi\epsilon_0h^2## and when i use that instead of ##Q_{max}## i get that ##F_{max}=(E_{crit})^2h^216\pi\epsilon_0##

And somehow my book gives this answer:

$$F_{max}=\pi\epsilon_0a^4(E_{crit})^2/h^2$$ How did they include ##a## and why is it divided by ##h^2## I don't understand their solution, can you make something out of it?