An electron is found to repel another electron at a distance of 1 cm with a force F = 2.3 × 10-24 N. Two protons placed at a distance of 5 cm will
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → repel each other with a force F = 9.2 × 10-26 N
The electrostatic force between two charges is given by Coulomb’s law. A proton carries charge +e, of the same magnitude as the electron’s charge, so the two protons feel the same force law as the two electrons; like charges repel.
\( \displaystyle F = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r^{2}} \Rightarrow F \propto \frac{1}{r^{2}} \text{ for the same charges} \)
\( \displaystyle \frac{F'}{F} = \left(\frac{r}{r'}\right)^{2} = \left(\frac{1\,\mathrm{cm}}{5\,\mathrm{cm}}\right)^{2} = \frac{1}{25} \)
\( \displaystyle F' = \frac{2.3\times10^{-24}\,\mathrm{N}}{25} = 9.2\times10^{-26}\,\mathrm{N} \)
The distances appear only as a ratio, so they need not be converted to metres.