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

Capacitance = Co= 5 pF

Separation between the plates = d = 1 mm.=1*10^-3 m

The electric field in the region between the plates =E= 3.00×10^4 V/m

Potential difference =V =Ed= 30 V

A) Maximum magnitude of charge =q=CV=[5*10^-12]*30

q = 1.5*10^-10 C


B) A dielectric with a dielectric constant of 100 is inserted between the plates

the maximum magnitude of charge on each plate =Q =(dilectric const)CV= 1.5*10^-8 C

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