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

The Correct Option is C

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