Dry air will break down if the electric field exceeds 3.0 x 10^6 V/m. If the ele

Question

Dry air will break down if the electric field exceeds 3.0 x 10^6 V/m. If the electric field exceeds this value, a current can form, generating a spark. What amount of charge can be placed on a circular plate capacitor before reaching this maximum electric field strength if the diameter of each place is 6.0 cm? Assuming nothing else changes, what would be the charge if a piece of Quartz were inserted into the capacitor (Dielectric constant = 4.3)? Please show equations used and solve step by step.

Explanation / Answer

We know that

Q = C*V

C = e0*A/d

V = E*d

Q = (e0*A/d)*(E*d)

Q = e0*A*E = e0*pi*d^2*E/4

Using given values:

Q = 8.85*10^-12*pi*0.06^2*3*10^6/4

Q = 7.51*10^-8 C

Part B.

If quartz is inserted, then

C = k*e0*A/d

then

Q = k*e0*pi*d^2*E/4

Using given values:

Q = 4.3*8.85*10^-12*pi*0.06^2*3*10^6/4

Q = 3.23*10^-7 C

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