A) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{q}{R} \right)\]
B) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{R}-\frac{Q}{r} \right)\]
C) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{Q}{R} \right)\]
D) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{Q}{R}-\frac{q}{r} \right)\]
Correct Answer: A
Solution :
The potential \[{{V}_{1}}\]of smaller sphere is given by \[{{V}_{1}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{r}+\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{R}\] The potential \[{{V}_{2}}\]of bigger sphere is given by \[{{V}_{2}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{R}+\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{R}\] So, the potential difference between the plates \[V={{V}_{1}}-{{V}_{2}}\] or\[V=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{r}+\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{R}-\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{R}-\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{R}\]\[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{r}-\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{R}=\frac{1}{4\pi {{\varepsilon }_{0}}}\left( \frac{q}{r}-\frac{q}{R} \right)\]You need to login to perform this action.
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