A) \[\frac{{{q}_{1}}}{4\pi {{\varepsilon }_{0}}a}-\frac{{{q}_{2}}}{4\pi {{\varepsilon }_{0}}b}\]
B) \[\frac{{{q}_{2}}}{4\pi {{\varepsilon }_{0}}}\left( \frac{1}{a}-\frac{1}{b} \right)\]
C) \[\frac{{{q}_{1}}}{4\pi {{\varepsilon }_{0}}}\left( \frac{1}{a}-\frac{1}{b} \right)\]
D) None of these
Correct Answer: C
Solution :
The potential on the surface of the sphere 1 is given by \[{{V}_{1}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}}{a}+\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{2}}}{b}\] ?..(i) The potential on the surface of the sphere 2 is given by \[{{V}_{2}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}}{a}+\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{2}}}{p}\] ?..(ii) Now potential difference, \[V={{V}_{1}}-{{V}_{2}}\] \[\Rightarrow \] \[V=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}}{a}-\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}}{b}\] \[\Rightarrow \] \[V=\frac{{{q}_{1}}}{4\pi {{\varepsilon }_{0}}}\left( \frac{1}{a}-\frac{1}{b} \right)\]
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