Question

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

• A. Q
• B. $\frac{3Q}{4}$
• C. $\frac{Q}{2}$
• D. $\frac{Q}{3}$

Answer 1

Answer: (C)

$\frac{Q}{2}$

Answer 2

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 $q=\frac{Q}{2}$ for the maximum force) $=\frac{1}{4\, \pi\, \varepsilon_{0}} \cdot \frac{\frac{Q}{2}\left(\frac{Q}{2}\right)}{r^{2}}$ $=\frac{1}{4 \,\pi\, \varepsilon_{0}} \cdot \frac{\frac{Q^{2}}{4}}{r^{2}}$ $=\frac{1}{4 \,\pi \,\varepsilon_{0}} \cdot \frac{Q^{2}}{4 r^{2}}$ $=\frac{1}{4 \,\pi \,\varepsilon_{0}} \cdot \frac{\left(\frac{Q}{2}\right)^{2}}{r^{2}}$