A) \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\]
B) \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}-\frac{2q}{4\pi {{\varepsilon }_{0}}R}\]
C) \[\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}\]
D) \[\frac{(q+Q)}{4\pi {{\varepsilon }_{0}}R}\frac{2}{R}\]
Correct Answer: C
Solution :
[c] At P, potential due to shell |
\[{{V}_{1}}=\frac{q}{4\pi \,{{\varepsilon }_{0}}R}\] |
At P, due to charge |
\[{{V}_{2}}=\frac{Q}{4\pi {{\varepsilon }_{0}}\frac{R}{2}}\] |
\[=\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\] |
\[\therefore \] Net potential at P, |
\[V={{V}_{1}}+{{V}_{2}}=\frac{q}{4\pi {{\varepsilon }_{0}}R}+\frac{2Q}{4\pi {{\varepsilon }_{0}}R}\] |
(\[\because \] v is scalar quantity) |
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