Electrostatics Question 779
Question: Three concentric charged metallic spherical shells A, B and C have radii a, b and c; change densities $ \sigma ,-\sigma $ and $ \sigma $ and potentials $ V _{A},V _{B} $ and $ V _{C} $ respectively. Then which of the following relations is correct?
Options:
A) $ V _{A}=( a+b+c )\frac{\sigma }{{\varepsilon _{0}}} $
B) $ V _{B}=( \frac{a^{2}}{b}-b+c )\frac{\sigma }{{\varepsilon _{0}}} $
C) $ V _{C}=( \frac{a^{2}+b^{2}}{b}+c )\frac{\sigma }{{\varepsilon _{0}}} $
D) $ V _{A}=V _{B}=V _{C}=( a+b+c )\frac{\sigma }{{\varepsilon _{0}}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Potential due to a charged shell at an outside point
$ =\frac{1}{4\pi {\varepsilon _{0}}}\times \frac{Q}{r} $ While that inside the shell$ =\frac{\sigma R}{{\varepsilon _{0}}} $ ,
where R is the radius of the shell.
