In This post you will get answer of Q.
Three concentric spherical shells have radii a, b and c (a
AIPMTAIPMT 2009Electrostatic Potential and Capacitance
Report Error
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, $V _{ C }= V _{ A } neq V _{ B }$
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, $V _{ C }= V _{ A } neq V _{ B }$