A $$10 \ \mu$$C charge is divided into two parts and placed at $$1$$ cm distance so that the repulsive force between them is maximum. The charges of the two parts are:

Let the two parts be $$q$$ and $$(Q - q)$$ where $$Q = 10 \mu$$C.

The force between them: $$F = k\frac{q(Q-q)}{r^2}$$

For maximum force, we maximize $$q(Q-q)$$. Taking derivative and setting to zero:

$$\frac{d}{dq}[q(Q-q)] = Q - 2q = 0$$

$$q = \frac{Q}{2} = 5 \mu\text{C}$$

The two parts are $$5\mu$$C and $$5\mu$$C.

This matches option 3.

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