A) 4 : 1
B) 1 : 2
C) 2 : 1
D) 1 : 4
Correct Answer: A
Solution :
By connecting two surfaces with the help of a conductor wire, we make the potential of each of the surfaces equal remembering that electric field at a point is inverse proportional to the distance. When the two conducting spheres are connected by a conducting wire, charge will flow from one sphere (having higher potential) to other (having lower potential) till both acquire the same potential. \[{{V}_{1}}=\frac{kq}{{{r}_{1}}},{{V}_{2}}=\frac{kq}{{{r}_{2}}}\Rightarrow {{v}_{1}}={{v}_{2}}\] (according to question) \[\Rightarrow \] \[{{r}_{2}}=2{{r}_{1}},E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{r}^{2}}}\] So, \[\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}=4:1\]
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