Calculating electrostatic pressure

[June_cosmo]

Homework Statement

Calculating electrostatic pressure. A spherical balloon with radius 1.0 m is made of aluminum-coated Mylar. How many electrons must be deposited on the aluminum layer such that the resulting electric pressure is equal to one atmosphere?

Homework Equations

The Attempt at a Solution

Assume q is the total charge of electrons needed, on the sphere using Gauss's Law, $\vec E=\frac {q}{4\pi R^2 \epsilon}\hat r$. For one infinitesimal on sphere, $\vec F=\vec E*d_q, where F=F_{atmosphere}$
I checked out other questions and found this method may not be right..

 

[andrevdh]

Maybe it is similar to the process of pressurizing a balloon by adding more and more gas to it it, that is the "electric pressure" increases as more and more electrons are brought onto the surface of the balloon? According to Wiki an electrostatic pressure is exerted on a section of a surface charge on a conductor due to the electric field, E, at that point. Strangely enough it says that this pressure tends to push the surface charge into the conductor's surface? As far as I know the electric field is perpendicular to the surface of the conductor. Which makes this statement difficult to understand. I see that this problem is also discussed in the "Electrostatic pressure" Similar discussion link below.

 

[rude man]

The charges all repel each other so it is clear that there is a force acting to push the balloon's surface outward. For example, think of a thin strip about the "equator" - all the charges repel each other so they're trying to get away from each other radially outwards. (That's why, on a charged solid sphere, they're all on the ouside surface!)

OK, as to the quantitaive aspect - I suggest considering virtual work! From an energy viewpoint this is not a difficult problem.