Rankers Physics

Coulomb's Law: Practice Problem & Solution

5. 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): (2010 Pre)
$\frac{4\pi\epsilon_0 F d^2}{q^2}$
$\frac{4\pi\epsilon_0 F d^2}{e^2}$
$\sqrt{\frac{4\pi\epsilon_0 F d^2}{q^2}}$
$\sqrt{\frac{4\pi\epsilon_0 F d^2}{e^2}}$

Solution Explained:

To solve this problem, we apply the core principles of Coulomb's Law. Understanding the underlying formula is key to arriving at the correct answer below:

Coulomb force $F = \frac{1}{4\pi\epsilon_0} \frac{q^2}{d^2}$, so $q = \sqrt{4\pi\epsilon_0 F d^2}$. Number of missing electrons is $n = \frac{q}{e} = \sqrt{\frac{4\pi\epsilon_0 F d^2}{e^2}}$.

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