Two point charges +5 \( \mu\mathrm{C} \) and -5 \( \mu\mathrm{C} \) are placed at O (0 mm, 0 mm) and P(3 mm, 4 mm) respectively force on +5 \( \mu\mathrm{C} \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 1.8(3\hat{\imath} + 4\hat{\jmath})\times10^{3}\,\mathrm{N} \)
By Coulomb's law the magnitude of the force is \( F = kq_1q_2/r^2 \). The charges are unlike, so the force on the charge at O is attractive, directed from O towards P.
\( \displaystyle r = \sqrt{3^2 + 4^2}\,\mathrm{mm} = 5\,\mathrm{mm} = 5\times10^{-3}\,\mathrm{m} \)
\( k = 9\times10^{9}\,\mathrm{N\,m^2\,C^{-2}} \)
\( \displaystyle F = \frac{9\times10^{9}\times(5\times10^{-6})\times(5\times10^{-6})}{(5\times10^{-3})^2} = \frac{0.225}{25\times10^{-6}} = 9\times10^{3}\,\mathrm{N} \)
The unit vector from O towards P is
\( \displaystyle \hat{r} = \frac{3\hat{\imath} + 4\hat{\jmath}}{5} \)
\( \displaystyle \vec{F} = 9\times10^{3}\times\frac{3\hat{\imath} + 4\hat{\jmath}}{5} = 1.8(3\hat{\imath} + 4\hat{\jmath})\times10^{3}\,\mathrm{N} \)