Q67 / 90 · JEE Main 2012 (26 May Online) · Physics

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 farad using a conducting material. Statement 2: It is possible for earth as its radius is $6.4 \times 10^6 \mathrm{~m}$.

  • 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.
  • Correct answer
    D
    Statement 1 is true, Statement 2 is false.

Solution

Capacitance of sphere is given by: $C=4 \pi \epsilon_0 r$ If, $C=1 \mathrm{~F}$ then radius of sphere needed: $r=\frac{C}{4 \pi \epsilon_0}=\frac{1}{4 \pi \times 8.85 \times 10^{-12}}$ or, $r=\frac{10^{12}}{4 \pi \times 8.85}=9 \times 10^9 \mathrm{~m}$ $9 \times 10^9 \mathrm{~m}$ is very large, it is not possible to obtain such a large sphere. Infact earth has radius $6.4 \times 10^6 \mathrm{~m}$ only and capacitance of earth is $711 \mu \mathrm{F}$.

Hence, the correct answer is option: 'D'.

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