> Q. Three concentric spherical shells have radii a, b and c (a AIPMTAIPMT 2009Electrostatic Potential and Capacitance Report Error – LIVE ANSWER TODAY

Q. Three concentric spherical shells have radii a, b and c (a AIPMTAIPMT 2009Electrostatic Potential and Capacitance Report Error

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Three concentric spherical shells have radii a, b and c (a

AIPMTAIPMT 2009Electrostatic Potential and Capacitance

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Solution:

$q _{ A } =4 pi a ^{2} sigma$

$q _{ B } =-4 pi b ^{2} sigma$

$q _{ C }=4 pi c ^{2} sigma,, c = a + b$

$V _{ A } =frac{1}{4 pi in_{0}}left(frac{ q _{ A }}{ a }+frac{ q _{ B }}{ b }+frac{ q _{ C }}{ c }right)$

$=frac{2 sigma a }{epsilon_{0}}$

$V _{ B } =frac{1}{4 pi in_{0}}left(frac{ q _{ A }}{ a }+frac{ q _{ B }}{ b }+frac{ q _{ C }}{ c }right)$

$=frac{sigma}{epsilon_{0}}left(frac{ a ^{2}}{ b }- b + c right)$

$=frac{sigma}{epsilon_{0}}left( a +frac{ a ^{2}}{ b }right)$

$V _{ C } =frac{1}{4 pi in_{0}}left(frac{ q _{ A }}{ a }+frac{ q _{ B }}{ b }+frac{ q _{ C }}{ c }right)$

$=frac{sigma}{epsilon_{0}}left(frac{ a ^{2}- b }{ c }+ c right)=frac{2 sigma a }{epsilon_{0}}$

So, $V _{ C }= V _{ A } neq V _{ B }$

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