Question

A charge of $0.8$ coulomb is divided into two charges $Q_1$ and $Q_2$. These are kept at a separation of $30cm$. The force on $Q_1$ is maximum when

• A. $Q_1=Q_2=0.4C$
• B. $Q_1\approx 0.8C,Q_2$ negligible
• C. $Q_1$ negligible, $Q_2\approx 0.8C$
• D. $Q_1=0.2C,Q_2=0.6C$

Answer 1

Answer: (A)

Checking the given options one by one
(i) $Q_1=Q_2=0.4C$.
The force on $Q_1$ due to $Q_2$
$F=k_p\frac{Q_1\times Q_2}{30\times 10^{-2}}$
$=k\frac{Q_1{Q}_2\times 100}{30}$
$=k\frac{0\cdot 4\times 0.4\times 100}{30}$
$=\frac{k\times 0\cdot 16\times 100}{30}$
(ii) When
$Q_1=0\cdot 8C{Q}_2\approx 0$
$F=\frac{k\times Q_1{Q}_2}{30\times 10^{-2}}\approx 0$
(iii) when $Q_1\approx 0,Q_2=0\cdot 8C$ $F=0$
(iv) $Q_1=0\cdot 2C{Q}_2=0\cdot 6C$
$F=\frac{k\cdot 0\cdot 2\times 0\cdot 6}{30\times 10^{-2}}$
$=\frac{k\times 0\cdot 12\times 10^2}{30}$
Thus we find that, in option(a), the force on $Q_1$ will be maximum.
$\therefore$ correct answer is $Q_1=Q_2=0\cdot 4C$