JEE Main On 08 April 2018 Question 17
Question: Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $ \text{+ }\sigma $ , $ \text{- }\sigma $ and $ \text{+ }\sigma $ respectively. The potential of shell B is: [JEE Main Online 08-04-2018]
Options:
A) $ \frac{\sigma }{{\in_O}}[ \frac{b^{2}-c^{2}}{b}+a ] $
B) $ \frac{\sigma }{{\in_O}}[ \frac{b^{2}-c^{2}}{c}+a ] $
C) $ \frac{\sigma }{{\in_O}}[ \frac{a^{2}-b^{2}}{a}+c ] $
D) $ \frac{\sigma }{{\in_O}}[ \frac{a^{2}-b^{2}}{b}+c ] $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ V _{B}=\frac{a^{2}\sigma }{{\in_0}b}-\frac{b^{2}\sigma }{{\in_0}b}+\frac{c^{2}\sigma }{{\in_0}c}=\frac{\sigma }{{\in_0}}[ \frac{a^{2}-b^{2}}{b}+c ] $
