question_answer

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force F between the two is :-

A)  \[K\frac{{{e}^{2}}}{{{r}^{2}}}\hat{r}\]                              

B)  \[-K\frac{{{e}^{2}}}{{{r}^{3}}}\hat{r}\]

C)                  \[K\frac{{{e}^{2}}}{{{r}^{3}}}\vec{r}\]                   

D)  \[-K\frac{{{e}^{2}}}{{{r}^{3}}}\vec{r}\] (Where \[K=\frac{1}{4\pi {{\varepsilon }_{0}}}\])

Correct Answer: D

Solution :

Coulomb force  \[=\frac{k{{e}^{2}}}{{{r}^{2}}}(-\,\hat{r})\]                 \[=-\frac{k{{e}^{2}}}{{{r}^{3}}}\vec{r}\]