A) \[\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{e}^{2}}}\]
B) \[\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{e}^{2}}}{{{d}^{2}}}}\]
C) \[\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{e}^{2}}}}\]
D) \[\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{q}^{2}}}\]
Correct Answer: C
Solution :
Two positive ions each carrying a charge q are kept at a distance d, then it is found that force of repulsion between them is \[F=\frac{kqq}{{{d}^{2}}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{qq}{{{d}^{2}}}\] where \[q=ne\] \[\therefore \] \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{n}^{2}}{{e}^{2}}}{{{d}^{2}}}\] \[\Rightarrow \] \[n=\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{d}_{2}}}{{{e}^{2}}}}\]
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