A charge $Q$ is divided into two charges $q$ and $Q-q$. The value of $q$ such that the force between them is…
A charge $Q$ is divided into two charges $q$ and $Q-q$. The value of $q$ such that the force between them is maximum, is
- $Q$
- $\frac{3 Q}{4}$
- $\frac{Q}{2}$
- $\frac{Q}{3}$
Solution
By Coulomb's law,
When charge $Q$ is divided into two charges $q$ and $Q-q$
$
F=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q \cdot(Q-q)}{r^2}
$
The value of $q$
$
F_{\max }=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\frac{Q}{2}\left(Q-\frac{Q}{2}\right)}{r^2}
$
(Putting $q=\frac{Q}{0}$ for the maximum force)
$
\begin{aligned}
& =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\frac{Q}{2}\left(\frac{Q}{2}\right)}{r^2} \\
& =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\frac{Q^2}{4}}{r^2} \\
& =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Q^2}{4 r^2} \\
& =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\left(\frac{Q}{2}\right)^2}{r^2}
\end{aligned}
$
So, option (3) is correct
Asked in: AP EAMCET 2014
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