A capacitor is formed from two concentric spherical conducting shells separated
ID: 1333026 • Letter: A
Question
A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 11.0 cm , and the outer sphere has radius 15.5 cm . A potential difference of 140 V is applied to the capacitor.
(A)What is the energy density at r= 11.1 cm , just outside the inner sphere?
(B)What is the energy density at r = 15.4 cm , just inside the outer sphere?
(C)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 or No?
Explanation / Answer
here,
C = 4*pi*epsilon0/(1/a - 1/b)
C = 4 * pi*8.85*10^-12 /(1/0.11 - 1/0.155)
C = 4.21 *10^-11 F
voltage , V = 140 V
Q = C*V
Q = 140 * 4.21 *10^-11
Q = 5.89*10^-9 C
(a)
electric feild at r=11.1 cm, E =Q/ 4*pi*epsilon0 *r^2
E = 5.89*10^-9 /(4 * pi * 8.85*10^-12 * 0.111^2)
E = 4298.49 N/C
energy density , D = e0 * E^2 /2
D = 8.85*10^-12 *4298.49^2 /2
D = 1.64 *10^-4 J/m^3
the energy density at r = 11.1 cm is 1.64 *10^-4 J/m^3
(b)
electric feild at r=11.1 cm, E =Q/ 4*pi*epsilon0 *r^2
E = 5.89*10^-9 /(4 * pi * 8.85*10^-12 * 0.155^2)
E = 2204.44 N/C
energy density , D = e0 * E^2 /2
D = 8.85*10^-12 *2204.44^2 /2
D = 4.3 *10^-5 J/m^3
the energy density at r = 11.1 cm is4.3 *10^-5 J/m^3
(c)
no this is not true for spherical capacitor , as energy density is different at different distances from the centre
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