Question

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

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

Answer 1

Answer: (A)

Checking the given options one by one
(i) $Q_{1}=Q_{2}=0.4 C$.
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 8 C Q_{2} \approx 0 $
$F =\frac{k \times Q_{1} Q_{2}}{30 \times 10^{-2}} \approx 0$
(iii) when $Q_{1} \approx 0, Q_{2}=0 \cdot 8 C$ $F=0$
(iv) $Q_{1}=0 \cdot 2 C Q_{2}=0 \cdot 6 C$
$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 $Q_{1}=Q_{2}=0 \cdot 4 C$