Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular aluminum plates, each 19 cm in diameter, separated by 1.0 cm. how much charge can be added to each of the plates before a spark jumps between the two plates? for such flat electrodes, assume that value of 3×106n/c of the field causes a spark. express your answer with the appropriate units.

Explanation:

The capacitance of a parallel-plate capacitor is given by

where is the vacuum permittivity, A is the surface area of the plates, d their separation.

We also know the following relationship

where Q is the charge stored on the capacitor and V the potential difference between the plates.

Combining the two equations,

We also know that for a uniform electric field (such as the one between the plates of a parallel-plate capacitor), we have

where E is the magnitude of the electric field. Substituting into the previous equation and re-arranging it,

For the capacitor in the problem:

is the area of the plates

is the maximum electric field before a spark is produced

Solving for Q, we find the maximum charge that can be added before that occurs:

it has to be b, about 97 percent.