# 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 m

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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)
1. $\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}$
2. $\sqrt {\frac{{4\pi {\varepsilon _0}F{e^2}}}{{{d^2}}}}$
3. $\sqrt {\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}}$
4. $\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{q^2}}}$

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Correct Answer - Option 3 : $\sqrt {\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}}$

Concept:

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:

$F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left( q \right)\left( q \right)}}{{{d^2}}}$

$F = \frac{{{q^2}}}{{4\pi {\varepsilon _0}{d^2}}}$  ---(1)

q = ne

n = number of electrons missing from each ion

e = magnitude of charge on electron

Analysis:

Rearranging Equation (1), we get:

${q^2} = 4\pi {\varepsilon _0}F{d^2}$

$q = \sqrt {4\pi {\varepsilon _0}F{d^2}}$

With q = ne

$n = \frac{q}{e} = \sqrt {\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}}$