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QAIPMT-2009-Ph-2173: NEET 2009 Physics - Class 12 AIPMT-2009-Ph-2173 Solution: Three concentric spherical shells have radii a, b and c (a < b…
Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities and respectively. If , and denote the potentials of the three shells, then, for c = a + b, we have
Multiple Choice Options
- A
- B
- C
- D
Step-by-Step Verified Solution
V A = 1 4 � _ 0 { q A a + q B b + q C c }
= 4 � 4 � _ 0 { a 2 _ a _ b 2 _ b + c 2 _ c }
V A = 1 _ 0 { a 2 _ a _ b 2 _ b + c 2 _ c }
V B = 1 _ 0 { a 2 _ a _ b 2 _ b + c 2 _ c }
V C = 1 _ 0 { a 2 _ a _ b 2 _ b + c 2 _ c }
Given c = a + b.
If a = a, b = 2a and c = 3a for example, as c > b > a,
V A = 1 _ 0 { a 2 _ a _ 4 b 2 _ 2 a + c 2 _ c }
V B = 1 _ 0 { a 2 _ 2 a _ 4 a 2 _ 2 a + c 2 _ c }
V C = 1 _ 0 { a 2 _ 3 a _ 4 a 2 _ 3 a + c 2 _ c }
It can seen by taking out common factors that
V A = V C > V B i.e., V A = V C � V B