Electrostatics Question 680
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 of an electron)
Options:
A) $ \frac{4\pi {\varepsilon _{0}}Fd^{2}}{e^{2}} $
B) $ \sqrt{\frac{4\pi {\varepsilon _{0}}Fe^{2}}{d^{2}}} $
C) $ \sqrt{\frac{4\pi {\varepsilon _{0}}Fd^{2}}{e^{2}}} $
D) $ \frac{4\pi {\varepsilon _{0}}Fd^{2}}{q^{2}} $
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Answer:
Correct Answer: 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}=ne $
$ \therefore n=\sqrt{\frac{4\pi {\varepsilon _{0}}Fd^{2}}{e^{2}}} $
