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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)
A
$\frac{4\pi\varepsilon_0Fd^2}{q^2}$
B
$\frac{4\pi\varepsilon_0Fd^2}{e^2}$
C
$\sqrt{\frac{4\pi\varepsilon_0Fe^2}{d^2}}$
D
$\sqrt{\frac{4\pi\varepsilon_0Fd^2}{e^2}}$
Detailed Solution
If n electrons are missing from each ion, its charge is q = ne.
Coulomb's law: $F = \frac{1}{4\pi\varepsilon_0}\frac{q^2}{d^2} = \frac{1}{4\pi\varepsilon_0}\frac{n^2e^2}{d^2}$
$n^2 = \frac{4\pi\varepsilon_0Fd^2}{e^2}$
$n = \sqrt{\frac{4\pi\varepsilon_0Fd^2}{e^2}}$
Coulomb's law: $F = \frac{1}{4\pi\varepsilon_0}\frac{q^2}{d^2} = \frac{1}{4\pi\varepsilon_0}\frac{n^2e^2}{d^2}$
$n^2 = \frac{4\pi\varepsilon_0Fd^2}{e^2}$
$n = \sqrt{\frac{4\pi\varepsilon_0Fd^2}{e^2}}$