Q: 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) $\large \frac{4\pi \epsilon_0 F d^2}{q^2} $

(b) $\large \frac{4\pi \epsilon_0 F d^2}{e^2} $

(c) $\large \sqrt{\frac{4\pi \epsilon_0 F d^2}{q^2}} $

(d) $\large \sqrt{\frac{4\pi \epsilon_0 F d^2}{e^2}} $

Ans: (d)

Sol: $\large F = \frac{1}{4\pi \epsilon_0} \frac{q^2}{d^2}$

$\large q = \sqrt{4\pi \epsilon_0 d^2 F}$

$\large n e = \sqrt{4\pi \epsilon_0 d^2 F}$

$\large n = \sqrt{\frac{4\pi \epsilon_0 F d^2}{e^2}} $