An infinite line of charge has a linear charge density of \( 10^{-7}\,\mathrm{C\,m^{-1}} \). The magnitude of the force acting on a charge \( 6.4 \times 10^{-19}\,\mathrm{C} \) kept at a distance of 8 cm from the line of charge is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1.44 \times 10^{-14}\,\mathrm{N} \)
The field of an infinite line charge (from Gauss's law) is \( E = \lambda/(2\pi\varepsilon_0 r) = 2k\lambda/r \), and the force on a charge \( q \) is \( F = qE \).
\( r = 8\,\mathrm{cm} = 0.08\,\mathrm{m} \)
\( k = 9\times10^{9}\,\mathrm{N\,m^{2}\,C^{-2}} \)
\( \displaystyle E = \frac{2 \times 9\times10^{9} \times 10^{-7}}{0.08} = 2.25\times10^{4}\,\mathrm{N\,C^{-1}} \)
\( \displaystyle F = qE = 6.4\times10^{-19} \times 2.25\times10^{4} = 1.44\times10^{-14}\,\mathrm{N} \)