Question

Two positive ions, each carrying a charge $q$, are separated by a distance $d$. If $F$ is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

• A. $\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}$
• B. $\sqrt{\frac{4\pi {\epsilon }_{0}F{e}^2}{d^2}}$
• C. $\sqrt{\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}}$
• D. $\frac{4\pi {\epsilon }_{0}F{d}^2}{q^2}$

Answer 1

Answer: (C)

According to Coulomb's law, the force of repulsion between the two positive ions each of charge $q$, separated by a distance $d$ is given by
$F=\frac{1}{4\pi {\epsilon }_0}\frac{(q)(q)}{d^2}$
$F=\frac{q^2}{4\pi {\epsilon }_0{d}^2}$
$q^2=4\pi {\epsilon }_{0}F{d}^2$
$q=\sqrt{4\pi {\epsilon }_{0}F{d}^2}$ ..(i)
Since, $q=ne$
where,
$n=$ number of electrons missing from each ion
$e=$ magnitude of charge on electron
$\therefore n=\frac{q}{e}$
$n=\frac{\sqrt{4\pi {\epsilon }_{0}F{d}^2}}{e}$ (Using (i))
$=\sqrt{\frac{4\pi {\epsilon }_{0}F{d}^2}{e^2}}$