The capacitance of a spherical condenser is 1 | vedclass

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Question

(d) Given : $(b -a) = 1 	imes 10^{-3}\, m$ ..... $(i)$
and $C = 4\pi {\varepsilon _0}\left( {\frac{{ab}}{{b - a}}} ight) = 1 	imes {10^{ - 6}}$

Vedclass · Accepted Answer

$3\,m$

Vedclass · Answer

(d) Given : $(b -a) = 1 	imes 10^{-3}\, m$ ..... $(i)$
and $C = 4\pi {\varepsilon _0}\left( {\frac{{ab}}{{b - a}}} ight) = 1 	imes {10^{ - 6}}$
$==>$ $1 	imes {10^{ - 6}} = \frac{1}{{9 	imes {{10}^9}}}\left( {\frac{{ab}}{{{{10}^{ - 3}}}}} ight)$
$==>$ $ab = 9$ ..... $(ii)$
From equations $(i)$ and $(ii)$
$b - \frac{9}{b} = \frac{1}{{1000}}$ $==>$ $1000 b^2 -b -9000 = 0$
$==>$ $b = \frac{{1 \pm \sqrt {{{( - 1)}^2}\, - \,4(1000)\,( - \,9000)} }}{{2 	imes 1000}}$
{Solving of quadratic equation}
$==>$ $b = \frac{{1 \pm \sqrt {36 	imes {{10}^6}} }}{{2000}} \approx \,\frac{{\sqrt {36 	imes {{10}^6}} }}{{2000}} = 3\,m.$

The capacitance of a spherical condenser is $1\,\mu F$. If the spacing between the two spheres is $1\,mm$, then the radius of the outer sphere is

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