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Surface force on electrically charged balloon

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A balloon made of light conducting material could be kept approximately spherical by connecting it to a high voltage supply.

The balloon has radius 0.05 m, and the dielectric breakdown field to produce spark in air is E_b = 3?10^6 V/m
a) What is the maximum permissible voltage?
b) What gas pressure, in atmospheres, inside the balloon would have the same effect?
c) How large could the surface mass density of the balloon be?

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Surface force on electrically charged balloon is discussed.

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Solution:

(a)
A conducting sphere of radius R with electric charge Q on it has potential

V_s = Q / (4πε_oR),

Where

ε_o = 8.85?10^{-12} C^2/(N m^2)

is the permittivity of vacuum.

The electric field at the surface of the sphere is

E_s = Q / (4πε_oR^2) = V_s/R

If we require that the electric field is at most at the dielectric breakdown,

E_b = E_s ...

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