A) \[{{\left( {{R}_{1}}\text{/}{{R}_{2}} \right)}^{2}}\]
B) \[\left( {{R}_{2}}\text{/}{{R}_{1}} \right)\]
C) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3}}\]
D) \[{{R}_{1}}/{{R}_{2}}\]
Correct Answer: A
Solution :
Let \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] are the charge densities of two sphere. Then, \[{{E}_{1}}=\frac{{{\rho }_{1}}{{R}_{1}}}{3{{\varepsilon }_{0}}}\,\,and\,\,{{E}_{0}}=\frac{{{\rho }_{2}}{{R}_{2}}}{3{{\varepsilon }_{0}}}\] \[\because \,\,\,\,\,\,\,\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{\rho }_{1}}{{R}_{1}}}{{{\rho }_{2}}{{R}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\] \[\therefore \,\,\,\,\,\,\,{{\rho }_{1}}={{\rho }_{2}}=\rho \] So, \[{{V}_{1}}=\frac{\rho R_{1}^{2}}{3{{\varepsilon }_{0}}}\] and \[{{V}_{2}}=\frac{\rho R_{2}^{2}}{3{{\varepsilon }_{0}}}\] \[\therefore \,\,\,\,\,\,\,\,\,\frac{{{V}_{1}}}{{{V}_{2}}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
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