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

Answer 1

Answer: (C)

From Coulomb's law force of repulsion is
$F=k\frac{q^2}{d^2}\Rightarrow F=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{d^2}$
Where, $q=ne$
$\therefore F=\frac{1}{4\pi {ϵ}_0}\frac{n^2{e}^2}{d^2}\Rightarrow n=\sqrt{\frac{4\pi {ϵ}_{0}F{d}^2}{e^2}}$