A capacitor is formed from two concentric spherical conducting shells separated

Question

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 cm , and the outer sphere has radius 16.5 cm . A potential difference of 150 V is applied to the capacitor.

What is the energy density at r= 10.1 cm , just outside the inner sphere? in (J/m^3)

What is the energy density at r = 16.4 cm , just inside the outer sphere? in (J/m^3)

For a parallel-plate capacitor the energy density is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?

Yes /No?

Explanation / Answer

here,

V = 150 V
R1 = 10 cm = 0.1 m
R2 = 16.5 cm = 0.165 cm

Capacitance = 4pi*e0/(1/R1-1/R2)
C = (4 *3.14 *8.85 *10^-12)/(1/0.1-1/0.165)
C = 2.821 * 10^-11 F

Charge in capacitor is given as :

Q = C*V
Q = 2.821 * 10^-11 * 150
Q = 4.23 * 10^-9 C

A)
electric field = E = Q/(4*pi*e0*r^2)

E1 = (4.23 * 10^-9)/ (4*3.14*8.85*10^-12*0.1^2)

E1 = 3.805 * 10^3 J/m^3

B)

E2 = Q/(4*pi*e0*r^2)

E2 = (4.23 * 10^-9)/ (4*3.14*8.85*10^-12*0.165^2)

E2 = 1.397 * 10 ^3 J/m^3

C)

No

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