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)

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