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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

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

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