Question

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.5 cm, and the outer sphere has radius 16.5 cm. A potential difference of 150 V is applied to the capacitor. (a) What is the energy density at r = 10.6 cm, just outside the inner sphere

Answer 1

`U = 2.91 *10^(-5) J`

Step-by-step explanation:

energy density can be obtained as

`U = (1)/(2)\epsilon_o E^(2)`

Where,

E is electric field
`= (kQ)/(R^(2))`

K COLOUMB CONSTANT =8.99*10^{9} N -m2 /C2

Q is charge = CV

C is capacitance =
`4\pi \epsilon_o (r_1 r_2)/(r_2 -r_1)`

`=4\pi *8.85*10^(-12) [(10.5*16.5)/(16.5 -10.5)]`

`= 3.21*10^(-9) F`

`Q = 3.21*10^(-9) *150 = 4.81*10^{-7] C`

for r = 10.6 cm

`E = (8.99*10^(9)*3.21*10^(-9))/(0.106^(2))`

E = 2568.34 N/C

`U = (1)/(2)\epsilon_oE^(2)`

`U = (1)/(2)*8.85*10^(-12) *2568.34 ^2`

`U = 2.91 *10^(-5) J`