A solid conducting sphere of radius R_1 is surrounded by another … - Vidyadip

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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