Arcing in a parallel-plate air-filled capacitor

[The_Lobster]

I'm reading about constant-charge capacitor microphones, and they are essentially made up of a parallel-plate capacitor (one plate fixed, the other moving to sound pressure), in a circuit with a series resistor and DC source to provide polarising voltage.

The circuit is basically an RC filter, with a cut-off frequency down to 10-20Hz (so from f = 1/2piRC it requires a large R if C is small). The polarising voltage from the DC source is often around 48V, but can be as large as 200V for some microphones.

My question now is: The distance between the parallel plates in the capacitor is often around 20 micrometers. Now, if the dielectric strength of dry air is 3*10^6 V/m, there should be arcing at 3*10^6 V/m * 20 * 10^-6 m = 60 V. So from my theory it seems that most of these mics should arc due to the polarising voltage, just by turning them on! Clearly I must have a gap in my understanding some place?

Thanks!

 

[berkeman]

I'm reading about constant-charge capacitor microphones, and they are essentially made up of a parallel-plate capacitor (one plate fixed, the other moving to sound pressure), in a circuit with a series resistor and DC source to provide polarising voltage.

The circuit is basically an RC filter, with a cut-off frequency down to 10-20Hz (so from f = 1/2piRC it requires a large R if C is small). The polarising voltage from the DC source is often around 48V, but can be as large as 200V for some microphones.

My question now is: The distance between the parallel plates in the capacitor is often around 20 micrometers. Now, if the dielectric strength of dry air is 3*10^6 V/m, there should be arcing at 3*10^6 V/m * 20 * 10^-6 m = 60 V. So from my theory it seems that most of these mics should arc due to the polarising voltage, just by turning them on! Clearly I must have a gap in my understanding some place?

Thanks!

That's a good question! I don't think the inner space could be filled with partial vacuum (to take advantage of the Paschen curve) because that would inhibit the movement of the flexible plate. But what if it were filled with an inert gas? Would that raise the arc-over voltage enough?