Question

A 10 µC 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:

• A. 2 µC and 8 µC
• B. 3 µC and 7 µC
• C. 4 µC and 6 µC
• D. 5 µC and 5 µC

Answer 1

Answer: (D)

The charges are 5 µC each.

Answer 2

Let the two charges be $q$ and $10 - q$ µC. The repulsive force is proportional to the product:

$$F \propto q(10 - q)$$

To maximize $F$, maximize the product $q(10 - q)$.

Differentiate:

$$\frac{d}{dq}[q(10 - q)] = 10 - 2q = 0 \quad \Longrightarrow \quad q = 5 \, \mu C.$$

Thus, the charges are $5\, \mu C$ and $10 - 5 = 5\, \mu C$.