Three concentric, conducting spherical shells A, B and C have radii a = 10 cm, b = 20 cm and c = 30 cm respectively. The innermost shell A is earthed and charges q 2 = 4µC and q 3 = 3µC are given to shells B and C respectively. Calculate charge q 1 induced on shell A and energy stored in the system.
Text Solution
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Sol. System of three concentric shells is as shown in Fig. .
Fig.
Since, shell A is earthed, therefore its potential is zero. But its potential is
V = 
∴ 
= 0
or q 1 = – 3µC
Now, charges on different surfaces will be as shown in Fig. .
Fig.
To calculate energy stored in the system, it can be as considered in three parts:
(i) a spherical capacitor having radii a and b and having charge
| q 1 | = 3µC.
Its capacitance, C 1 = 
(ii) a spherical capacitor having radii b and c and having charge (q 2 + q 1 ) = 1µC.
Its capacitance, C 2 = 
(iii) an isolated sphere of radius c and having charge (q 3 + q 2 + q 1 ) = 4µC.
Its capacitance, C 3 = 4π ε 0 c
∴ Energy stored in the system
= 
+ 
+ 
= 0.45 joule
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