A certain charge Q is divided into two parts

Question:

A certain charge $\mathrm{Q}$ is divided into two parts $\mathrm{q}$ and (Q-q). How should the charges Q and $q$ be divided so that $\mathrm{q}$ and $(\mathrm{Q}-\mathrm{q})$ placed at a certain distance apart experience maximum electrostatic repulsion?

  1. $\mathrm{Q}=\frac{\mathrm{q}}{2}$

  2. $Q=2 q$

  3. $Q=4 q$

  4. $Q=3 q$


Correct Option: , 2

Solution:

$\mathrm{F}_{\mathrm{q}}=\frac{\mathrm{kq}(\mathrm{Q}-\mathrm{q})}{\mathrm{L}^{2}}=\frac{\mathrm{k}}{\mathrm{L}^{2}}\left(\mathrm{qQ}-\mathrm{q}^{2}\right)$

$\frac{\mathrm{dF}}{\mathrm{dq}}=0$ when force is maximum

$\frac{\mathrm{dF}}{\mathrm{dq}}=\frac{\mathrm{k}}{\mathrm{L}^{2}}[\overline{\mathrm{Q}}-2 \mathrm{q}]=0$

$\Rightarrow \mathrm{Q}-2 \mathrm{q}=0 \Rightarrow \mathrm{Q}=2 \mathrm{q}$

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