A) \[{{R}_{1}}/{{R}_{2}}\]
B) \[{{R}_{2}}/{{R}_{1}}\]
C) \[\sqrt{({{R}_{1}}/{{R}_{2}})}\]
D) \[R_{1}^{2}/R_{2}^{2}\]
E) \[R_{2}^{2}/R_{1}^{2}\]
Correct Answer: B
Solution :
\[\frac{{{q}_{1}}}{{{q}_{2}}}=\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\] and \[\frac{{{q}_{1}}}{{{q}_{2}}}=\frac{4\pi R_{1}^{2}{{\sigma }_{1}}}{4\pi R_{2}^{2}{{\sigma }_{2}}}\] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{4\pi R_{1}^{2}{{\sigma }_{1}}}{4\pi R_{2}^{2}{{\sigma }_{2}}}\] \[\therefore \] \[\frac{{{\sigma }_{1}}}{{{\sigma }_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\]
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