If the magnitude of the electric field in air exceeds roughly 3 ✕ 106 N/C, the air breaks down and a spark forms. For a two-disk capacitor of radius 50 cm with a gap of 2 mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other) ? The constant ε0 = 8.85 ✕ 10-12 C2 / (N·m2).

1.843 x 10^-5 C

Explanation:

Givens:

It is given that the air starts ionizing when the electric field in the air exceeds a magnitude of 3 x 10^6 N/C, which means that the max electric field can stand without forming a spark is 3 x 10^6 N/C.

Also it is given that the radius of the disk is 50 cm, it is required to find out the max amount of charge that the disk can hold without forming spark, which means the charge that would produce the max magnitude of the electric field that air can stand without forming spark, and since we know that the electric field in between 2 disk "Capacitor" is given by the following equation

E = (Q/A) / ∈o (1)

Where,

Q: total charge on the disk.

A: the area of the disk.

Calculations:

We want to find the quantity of charge on the disk that would produce an electric field of 3 x 10^6 N/C, knowing the radius of the disk we can find the cross-section of the disk, thus substituting in equation (1) we find the maximum quantity of charge the disk can hold

Q = EA∈o

= (3 x 10^6) x (π*0.50) x (8.85 x 10^-12)

= 1.843 x 10^-5 C

note:

calculations maybe wrong but method is correct