| This question has Statement 1 and Statement 2. [JEE ONLINE 26-05-2012] |
| 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\[6.4\times {{10}^{6}}m.\] |
A) Statement 1 is true, Statement 2 is true, and 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, and Statement 2 is not the correct explanation of Statement 1.
D) Statement 1 is true, Statement 2 is false.
Correct Answer: D
Solution :
| [d] Capacitance of sphere is given by: |
| \[C=4\pi {{\in }_{0}}r\] |
| If, C = 1F then radius of sphere needed: |
| \[r=\frac{C}{4\pi {{\in }_{0}}}=\frac{1}{4\pi \times 8.85\times {{10}^{-12}}}\] |
| or,\[r=\frac{{{10}^{12}}}{4\pi \times 8.85}=9\times {{10}^{9}}m\] |
| \[9\times {{10}^{9}}m\]is very large, it is not possible to obtain such a large sphere. In fact earth has radius \[6.4\times {{10}^{6}}m\]only and capacitance of earth is\[711\mu F.\] |
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