MCQ
A solid conducting sphere of radius $R_1$ is surrounded by another concentric hollow conducting sphere of radius $R_2$. The capacitance of this assembly is proportional to
  • A
    $\frac{{{R_2} - {R_1}}}{{{R_1}{R_2}}}$
  • B
    $\frac{{{R_2} + {R_1}}}{{{R_1}{R_2}}}$
  • C
    $\frac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}$
  • $\frac{{{R_1}{R_2}}}{{{R_2} - {R_1}}}$

Answer

Correct option: D.
$\frac{{{R_1}{R_2}}}{{{R_2} - {R_1}}}$
d
(d) Capacitance of the given assembly

$C = 4\pi {\varepsilon _0}\,\left( {\frac{{{R_1}{R_2}}}{{{R_2} - {R_1}}}} \right)$ 

==>$ C \propto \frac{{{R_1}{R_2}}}{{({R_2} - {R_1})}}$

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