A charge of 56 C is spread uniformly over a metallic thread of length 7 m and negligible cross-sectional area. What is the linear charge density of the thread?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 8\,\mathrm{C\,m^{-1}} \)
The linear charge density of a thin wire or thread is the charge per unit length, \( \lambda=Q/L \). The charge is spread uniformly, so the same value holds all along the thread.
\( \begin{aligned} \lambda &= \frac{Q}{L} \\ &= \frac{56\,\mathrm{C}}{7\,\mathrm{m}} \\ &= 8\,\mathrm{C\,m^{-1}} \end{aligned} \)
NCERT (2026-27):
Continuous Charge Distribution – “… The linear charge density λ of a wire is defined by
\( \displaystyle \lambda=\frac{\Delta Q}{\Delta l} \)\( \qquad (1.24) \)
where Δl is a small line element of wire on the macroscopic scale that, however, includes a large number of microscopic charged constituents, and ΔQ is the charge contained in that line element. The units for λ are C/m.”