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Question
Two charged particles placed at a separation of 20 cm exert 20 N of Coulomb force on each other. What will be the force of the separation is increased to 25 cm?
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Solution
Two charged particles placed at a separation of 20 cm exert 20 N of Coulomb force on each other.
So, \[F_1 = \frac{1}{4\pi \in_0} \cdot \frac{q^2}{r_1^2}\]
Also, \[F_2 = \frac{1}{4\pi \in_0} \cdot \frac{q^2}{r_2^2}\]
According to the question, we have :
\[\frac{F_2}{F_1} = \frac{r_1^2}{r_2^2}\]
\[ = \frac{20 \times 20}{25 \times 25} = \frac{16}{25}\]
\[ \therefore F_2 = \frac{16}{25} \times F_1\]
\[\Rightarrow F_2 = \frac{16}{25} \times 20 \]
\[ \Rightarrow F_2 = 12 . 8 N \approx 13 . 0 N\]
Therefore, the two charged particles will exert a force of 13.0 N on each other, if the separation is increased to 25 cm.
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