Please explain all steps. A parallel plate capacitor consists of two circular pl

Question

Please explain all steps.

A parallel plate capacitor consists of two circular plates each with a radius of 50cm. The plates are separated by a distance of 1mm. The potential difference between the plates is 12 volts. What is the capacitance of the system, when there is a vacuum in the region between the plates? What is the magnitude of the total charge on the positively charged plate? This capacitor initially has a potential difference of 12 volts across the plates, the system is isolated (not connected to a power supply). A dielectric material with dielectric constant kappa = 2. 0 is placed in between the plates. Does the potential difference across the plates change ? If so, find the new potential difference.

Explanation / Answer

C = eA/d = 8.85*10^-12 *pi.5^2/.001

C = 6.94 * 10^-9

b) Q = CV = 8.33*10^-8

c) new C will be

C' = kC = 13.88*10^-9

charge will be constant so voltage will change:

8.33*10^-8 = 13.88*10^-9 *V

v = 6 Volts

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