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 ___ ?

 An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force \( \vec{F} \) between the two is ___ ?

\( \left( \text{where } K = \frac{1}{4\pi \varepsilon_0} \right) \)

\( \text{(a)} \quad K \frac{e^2}{r^3} \vec{r} \)

\( \text{(b)} \quad K \frac{e^2}{r^2} \hat{r} \)

\( \text{(c)} \quad -K \frac{e^2}{r^3} \hat{r} \)

\( \text{(d)} \quad -K \frac{e^2}{r^3} \vec{r} \)

Answer : \( \text{(d)} \quad -K \frac{e^2}{r^3} \vec{r} \)

Concept: Relation between a vector, its magnitude and the unit vector needs to be understood. \( \vec{r} = r \hat{r} \)

\( F = K \frac{q_1 q_2}{r^2} \)

\( \vec{F} = K \frac{(+e)(-e)}{r^2} \hat{r} \)

\( \vec{F} = -K \frac{e^2}{r^2} \cdot \frac{\vec{r}}{r} \)

\( \vec{F} = -K \frac{e^2}{r^3} \vec{r} \)