Capacitance of a spherical condenser is 1,μ F . If spacing between two spheres is 1,mm , then radiu

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2. Electric Potential and Capacitance

hard

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

$30\,cm$

$6\,m$

$5\,cm$

$3\,m$

Solution

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

Standard 12

Physics

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