A) \[\frac{R_{2}^{2}}{R_{2}^{1}}\]
B) \[\frac{R_{1}^{2}}{R_{2}^{2}}\]
C) \[\frac{{{R}_{2}}}{{{R}_{1}}}\]
D) \[\frac{{{R}_{1}}}{{{R}_{2}}}\]
Correct Answer: C
Solution :
Fact: If sphere are joined, they acquire a common potential. If two spheres are joined charge flow till it is uniform both. the spheres, hence electric potential is same. \[\therefore \] \[{{V}_{1}}={{V}_{2}}\] \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}}{{{R}_{1}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{2}}}{{{R}_{2}}}\] \[\Rightarrow \] \[\frac{{{q}_{1}}}{{{R}_{1}}}=\frac{{{q}_{2}}}{{{R}_{2}}}\] ?.(i) Ratio of electric field is given by \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{q}_{1}}}{R_{1}^{2}}}{\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{q}_{2}}}{R_{2}^{2}}}\] \[\Rightarrow \] \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{q}_{1}}}{{{q}_{2}}}{{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}\] ?...(ii) Putting the value of \[\frac{{{q}_{1}}}{{{q}_{2}}}\]from equations (i) and (ii), we get \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{R}_{1}}}{{{R}_{2}}}\,\,{{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}=\frac{{{R}_{2}}}{{{R}_{1}}}\]You need to login to perform this action.
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