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 \varepsilon_0 F d^2 }{ e^2}$
• B. $ \sqrt{ \frac{ 4 \pi \varepsilon_0 F e^2 }{ d^2}}$
• C. $ \sqrt{ \frac{ 4 \pi \varepsilon_0 F d^2 }{ e^2}}$
• D. $ \frac{ 4 \pi \varepsilon_0 F d^2 }{ q^2}$

Answer 1

Answer: (C)

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{(q)(q)}{ d^2} $
$F = \frac{ q^2}{ 4 \pi \varepsilon_0 d^2} $
$ q^2 = 4 \pi \varepsilon_0 F \, d^2 $
$q = \sqrt{ 4 \pi \varepsilon_0 \, F \, d^2 } $ ..(i)
Since, $q = ne$
where,
$n =$ number of electrons missing from each ion
$e =$ magnitude of charge on electron
$ \therefore n = \frac{ q}{ e} $
$n = \frac{ \sqrt{ 4 \pi \varepsilon_0 F \, d^2 }}{ e} $ (Using (i))
$= \sqrt{ \frac{ 4 \pi \varepsilon_0 F \, d^2 }{ e^2 }} $