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The figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now if shell C is connected to shell A, then the final charge on the shell B is − Q x 11 , find the value of x .

Correct answer

8

Step-by-step solution

From given conditions, V A = V C and V B = 0 ⇒ V B = K ( Q − q 1 ) 3 a + K q 2 2 a + K q 1 2 a = 0 ⇒ 2 Q + q 1 + 3 q 2 = 0 ……(1) Using V C = V A ; K ( Q − q 2 ) 3 a + K q 2 3 a + K q 1 3 a = K q 1 a + K ( Q − q 1 ) 3 a + K q 2 2 a ⇒ q 1 = − q 2 4 …….(2) Using it in (1), q 2 = − 8 11 Q

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