A spherical capacitor is formed from two concentric spherical conducting shells

Question

A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has a radius of ra = 12.2 cm , and the outer sphere has a radius of rb= 15.0 cm . A potential difference of 120 V is applied to the capacitor.

A)

What is the capacitance of the capacitor?

Use 0 = 8.85×1012 F/m for the permittivity of free space.

B)

What is the magnitude E1 of the electric field E  at radius r= 12.7 cm , just outside the inner sphere?

C)

What is the magnitude of E  at r= 14.7 cm , just inside the outer sphere?

Explanation / Answer

capacitane = C = (4*pi*eo)/(1/ra-1/rb)

C = (4*pi*8.85*10^-12)/((1/0.122-1/0.15))

C = 7.26*10^-11 F

++++++++++++

B)

from gauss law

E*pi*r^2 = Q/eo = C*V/eo

E*2*pi*0.127^2 = (7.26*10^-11*120)/(8.84*10^-12)

E = 9725 N/C^2

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