A) \[+\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\]and \[-\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\]
B) \[+\frac{8\pi {{\varepsilon }_{0}}{{e}^{2}}}{r}\]and\[-\frac{4\pi {{\varepsilon }_{0}}{{e}^{2}}}{r}\]
C) \[-\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\]and \[-\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\]
D) \[+\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\]and \[+\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\]
Correct Answer: A
Solution :
P.E.\[=-\frac{k{{e}^{2}}}{r}=-\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\]; K.E.\[=-\frac{1}{2}(\text{P}\text{.E}\text{.})=\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\]
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