# Does the universe has a capacitance?

1. Mar 8, 2012

### shpongle

Does the universe has a capacitance?

2. Mar 8, 2012

### shpongle

The units of permittivity of space can be written as farads/meter.

3. Mar 8, 2012

### rbj

so, do we multiply $\epsilon_0$ by the number of meters across the known universe (which might be something like $c$ times 13.7 billion years)? is the capacitance of the universe growing as the universe expands?

4. Mar 9, 2012

### shpongle

That is what I meant.

I don't even know if it is a valid question but it occurred to me a few hours ago while I was trying to understand permittivity, which appears as a proportionality constant in the Gauss' Law.

5. Mar 9, 2012

### cmb

No, because it does not have an electrically contiguous surface.

The capacitance of a thing defines its electrical potential given a state of charge on it. As the charge cannot distribute itself on any 'universal' structure (as no such structure exists), so there can be no 'universal' capacitance.