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Electrostatic Energy of conducting shell and maximum electric field it can tolerate before breaking

Physics Asked on August 8, 2021

I stumbled upon an interesting phenomenon where the conducting shell can bear up to a certain limit of electric field before tearing apart.

Actually it is like a uncharged metallic shell put in a electric field say $E_0$ after increasing the field further the shell tears apart. For convenience radius of shell be $R_0$.

Now if we take a shell of $2R_0$, will we be able to find the maximum electric field that it can tolerate before tearing apart.

I have made the concept a question type to remove the constants like young’s modulus.

I was able to find that the concept is somewhere using the concept of electrostatic pressure i.e.
$$P= frac{sigma^2}{epsilon_0}$$P is electrostatic Pressure or the electrostatic energy of the shell.

So, the force must be
$$F=frac{sigma^2}{epsilon_0}times4pitimes R_0^2$$ For the initial case.

But the main problem is what ot d about the Surface charge density. How can we find that as it was initially uncharged.

My concepts or approach can be wrong if so then correct it please.

Thank you

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