Energy Stored leading to Dielectric breakdown

[HPRF]

Homework Statement

A cavity can only store 1J of EM energy as it reaches dielectric breakdown at 3kV/mm. What dielectric strength would a new gas filling the cavity have if the energy stored was to be 4J.

Homework Equations

U=\frac{1}{2}(epsilon)E²

The Attempt at a Solution

I would use the above equation to find the E field that would result in 4J of energy stored. Can anyone tell me if this is the correct approach to answering this question?

 

[BertHickman]

That's the correct approach. The energy scales as the E-field squared, so quadrupling the energy doubles the required E-field, so the gas dielectric must be able to withstand a field of 6 kV/mm without breaking down.