Question

The plates of a spherical capacitor have radii of 11.60 mm and 12.70 mm. Calculate the capacitance of the capacitor.

What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

If a 12.90 V potential is applied to the parallel-plate capacitor, calculate the magnitude of the electric field between the plates.

Calculate the energy density in the parallel-plate capacitor.

Answer 1

C = 4pieo (r)

C = 4*3.14* 8.85e-12 * (12.7-11.60mm)

C = 0.122 pF
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use C = eoA/d

A = 0.122e-12* (12.7-11.60)mm/8.85 e-12

A = 1.519 *10^-5 m^2
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E = V/d

E = 12.90/(12.7-11.6)mm

E = 1.1727*10^4 N/C or V/m
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energy density u = 0.5 eo E^2

u = 0.5 * 8.85e-12 * 1.1727*1.1727 *10^8

u = 6.08*10^-4 J/m^3
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