Question

A certain charge $Q$ is divide at first into two parts $\left(q\right)$ and $\left(Q-q\right).$ Later on the charges are placed at a certain distance. If the force of interaction between the two charges is maximum then:

• A. $\left(Q/q\right)=\left(4/1\right)$
• B. $\left(Q/q\right)=\left(2/1\right)$
• C. $\left(Q/q\right)=\left(3/1\right)$
• D. $\left(Q/q\right)=\left(5/1\right)$

Answer 1

The correct option is B $\left(Q/q\right)=\left(2/1\right)$

$F=\frac{K\left(Q-q\right)q}{r^2}=\frac{K}{r^2}\left(qQ-q^2\right)$

$\frac{df}{dq}=0,Q-2q=0$

$q=\frac{Q}{2}$

$\left(\frac{Q}{q}=\frac{2}{1}\right)$