Discussion
Which one of the following pairs of charges separated by the same distance r will experience a maximum force?
Answer: D
The maximum force is between 0.5 C and 0.5 C.
Every pair adds up to 1 C, and at the same separation Coulomb's force is proportional to the product \(q_{1}q_{2}\). For a fixed sum, the product is largest when the two parts are equal.
\[ \begin{aligned} 0.5 \times 0.5 &= 0.25 \\ 0.4 \times 0.6 = 0.24,\ 0.3 \times 0.7 &= 0.21 \\ 0.2 \times 0.8 = 0.16,\ 0.1 \times 0.9 &= 0.09 \end{aligned} \]
So the equal split gives the largest product and hence the largest force; the more unequal the split, the smaller the force.
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