This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1$ : It is not possible to make a sphere of capacity $1 \, F$ using a conducting material.
Statement $2$ : It is possible for Earth as its radius is $6.4 \times 10^6 \, m$.

  • A
    Statement $1$ is true,Statement $2$ is true,Statement $2$ is the correct explanation of Statement $1$.
  • B
    Statement $1$ is false,Statement $2$ is true.
  • C
    Statement $1$ is true,Statement $2$ is true,Statement $2$ is not the correct explanation of Statement $1$.
  • D
    Statement $1$ is true,Statement $2$ is false.

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Two spherical conductors of capacities $3 \mu F$ and $2 \mu F$ are charged to the same potential,having radii $3 \ cm$ and $2 \ cm$ respectively. If $\sigma_1$ and $\sigma_2$ represent the surface charge density on the respective conductors,then $\frac{\sigma_1}{\sigma_2}$ is:

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Match the following types of capacitors with their respective capacitance formulas:
Capacitor Type Capacitance Formula
$A$. Cylindrical capacitor $i$. $4\pi \epsilon_0 R$
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$C$. Parallel plate capacitor with dielectric $iii$. $\frac{2\pi \epsilon_0 \ell}{\ln(r_2/r_1)}$
$D$. Isolated spherical conductor $iv$. $\frac{4\pi \epsilon_0 r_1 r_2}{r_2 - r_1}$

The stratosphere acts as a conducting layer for the Earth. If the stratosphere extends up to $50 \ km$ from the Earth's surface,calculate the capacitance of the spherical capacitor formed between the Earth's surface and the stratosphere in $F$. Take the radius of the Earth as $6400 \ km$.

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