How much charge can be added to each of the plates before a spark jumps between the two plates? For such flat electrodes

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.

SOLUTION:

As you know that, parallel plate capacitance can be defined as

C=εo A/d

Where,

εo is the permittivity of free space constant, A is area of the capacitor plates, and d is the distance between them

Also, C= Q/V

where,

'Q' defines charge stored on the capacitor and 'V' express the potential difference between the plates.

Equating the equations.

εo A/d = Q/V

Q= (εo A V)/d

for a uniform electric field (such as the one between the plates of a parallel-plate capacitor)

V= Ed ->where 'E' defines magnitude of the electric field.

Therefore,

Q= (εo A E d)/d =>εo A E ->eq(1)

The area of the plates is given by

A= πr² => π(d/2)² =>π(0.19/2)

A=0.0284m²

Given: E= 3 x [tex]10^{6}[/tex] N/C

Substituting all the required values in eq(1)

(1)=> Q= (8.85x[tex]10^{-12}[/tex]) (-.0284)(3 x [tex]10^{6}[/tex] )

Q= 7.54 x[tex]10^{-7}[/tex] C

Therefore,7.54 x[tex]10^{-7}[/tex] C can be added to each of the plates before a spark jumps between the two plates