Question 244: Electrostatics & Capacitance

Question

Capacitance of an isolated conducting sphere of radius R
1
becomes n times when it is enclosed by a concentric conducting sphere of radius R
2
connected to earth. The ratio of their radii $$\left( {{{{R_2}} \over {{R_1}}}} \right)$$ is :

Accepted Answer

Initially $$ = {C_0} = 4\pi {\varepsilon _0}{R_1}$$
Finally $${{4\pi {\varepsilon _0}{R_1}{R_2}} \over {{R_2} - {R_1}}} = n{C_0} = 4\pi {\varepsilon _0}n{R_1}$$
$$ \Rightarrow $$ $${{{R_2}} \over {{R_2} - {R_1}}} = n$$
$$ \Rightarrow $$$$1 - {{{R_1}} \over {{R_2}}} = {1 \over n}$$
$$ \Rightarrow $$ $${{{R_1}} \over {{R_2}}} = {{n - 1} \over n}$$
$$ \Rightarrow $$ $${{{R_2}} \over {{R_1}}} = {n \over {n - 1}}$$

Answer

$${n \over {n - 1}}$$

Answer

$${{2n} \over {2n + 1}}$$

Answer

$${{n + 1} \over n}$$

Answer

$${{2n + 1} \over n}$$

Electrostatics & Capacitance

Capacitance of an isolated conducting sphere of radius R 1 becomes n times when it is enclosed by a concentric conducting sphere of radius R 2 connected to earth. The ratio of their radii $\left( {{{{R_2}} \over {{R_1}}}} \right)$ is :

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