Electric Charges And Fields Ques 43
43. 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 of an electron)
[2010]
(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) $\frac{4 \pi \varepsilon_0 F d^{2}}{q^{2}}$
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Answer:
Correct Answer: 43.(c)
Solution:
- (c) Let $n$ be the number of electrons missing. $F=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q^{2}}{d^{2}}$
$\Rightarrow q=\sqrt{4 \pi \varepsilon_0 d^{2} F}=n e$
$\therefore n=\sqrt{\frac{4 \pi \varepsilon_0 F d^{2}}{e^{2}}}$
If the charge of an electron $(=1.6 \times 10^{-19} C)$ is taken as elementary unit i.e., quanta of charge, the charge on any body will be some integral multiple of $e$
i.e., $Q= \pm n e$ where $n=1,2,3 \ldots$.
BETA
