# Maximum Permissible Voltage of a Sphere

1. Oct 15, 2009

### jmtome2

1. The problem statement, all variables and given/known data
It is suggested that a baloonmade of light conducting material could be kept approximately spherical by connecting it to a high voltage supply. The baloon has a diameter of 100 mm, and the maximum breakdown field in air is 3 megavolts/meter. What is the maximum permissible voltage?

2. Relevant equations
Voltage implies potential.

The potential outside of a sphere is $$V_{out}=\frac{Q}{4\pi\epsilon_0\cdot r}$$

3. The attempt at a solution
I think I should calculate the potential at the edge of the sphere, then compare that to some value based on the breakdown field?

Can someone explain what a breakdown field is and how it could be used in this situation? Wiki was fairly limited on this discussion.

2. Oct 15, 2009

### gabbagabbahey

The "breakdown field" is the strength of the eletric field at which the atoms in the air begin to ionize and conduct electricity. So, once you reach this field strength outside the balloon, it will become impossible to store more charge on the balloon-- the charge will simply leak off of it and conduct through the air to ground (like lightening). If you can't add more charge to the balloon, then you can't increase its potential (assuming the radius of the balloon is constant)...so when does the electric field outside first reach this value?

3. Oct 15, 2009

### jmtome2

when [tex]Q=0.000017\frac{coul}{m}[\tex]

Now I should go back and calculate V_in with this Q to find the maximum permissible voltage?

Last edited: Oct 15, 2009
4. Oct 15, 2009

### jmtome2

scratch that, lemme work on this somemore