Question

A charge $Q$is divided into $q$ and$(Q-q)$. If$Q/q=x$, such that the repulsion between them is maximum, find $x$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B

$2$

Step 1 : Given data

The charge $Q$ is divided into two equal parts of $Q$ and $Q-q$.

Step 2: To find the repulsive force

Repulsive force ,$F=\frac{kq\left(Q-q\right)}{d^2}$(here $d$ is the distance )

where $\left(k=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\right)$

Differentiate the above equation $\frac{dF}{dq}=\frac{k}{d^2}\left(Q-2q\right)$

$Q$ and $d$ are maximum for maximum force ,$\frac{dF}{dq}=0$

Step 3:To find the value of $x$

$$\begin{gathered} \frac{k}{d^2}\left(Q-2q\right)=0 \\ Q-2q=0 \\ \frac{Q}{q}=2 \end{gathered}$$

Hence the value of $x$ is $2$

So the correct answer is Option B