A parallel-plate capacitor has a capacitance of C_0 = 5 pF when there is air bet

Question

A parallel-plate capacitor has a capacitance of C_0 = 5 pF when there is air between the plates. The separation between the plates is 1 mm. (a) What is the maximum magnitude of charge that can be placed on each plate if the electric field in the region between the plates is not to exceed 30,000 V/m? [more than this, and a spark would cross the gap between plates] (b) A dielectric with a dielectric constant of 100 is inserted between the plates of the capacitor. completely filling the volume between the plates. Now what is the maximum magnitude of charge on each plate if the electric field between the plates is not to exceed 30.000 V/m

Explanation / Answer

(A) E_max = 30,000 V/m

Vmax = Emax d = 30,000 x 1 x 10^-3 m = 30 volt

Qmax = C Vmax =(5 pF) (30 V)

= 150 pC

(b) C = 100 C0 = 500 pF

Qmax = (500 pF) (30 V)

= 15000 pC

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