Students in an introductory physics lab are performing an experiment with a parallel-plate capacitor made of two circular aluminum plates, each 20 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, the field that causes a spark is at the high end of the range pre- sented in the chapter; assume a value of 3 * 106 N/C.

Q = 0.83 μC

Explanation:

Assuming that plates are much larger than the distance between them, we can think the electric field as constant and perpendicular to the outer surface of the plates.Applying Gauss' law to a rectangular surface half inside one of the plates and half outside it, since E and A are parallel each other, and E is zero on the other three faces, we can find the following expression for the electric field created by the charge on the plate:

     

Solving for Q, replacing E by the maximum electric field that doesn't cause the dielectric strength to break (3*10⁶ N/C), we get: