An infinitely long straight line carries a uniform linear charge density $\lambda =2\mu \text{C/m}$. Find the magnitude of the electric field at a point $5\text{cm}$ away from the line.

Step-by-step solution

1. Use the electric field expression for an infinite line charge: $E=\frac{\lambda }{2\pi {\epsilon }_{0}r}$.
2. Convert the given quantities: $\lambda =2\times 10^{-6}\text{C/m}$ and $r=0.05\text{m}$.
3. Substitute ${\epsilon }_0=8.85\times 10^{-12}{\text{C}}^2/{\text{N⋅m}}^2$ into the formula.
4. Calculate the denominator: $2\pi {\epsilon }_{0}r=2\pi \times 8.85\times 10^{-12}\times 0.05\approx 2.78\times 10^{-12}$.
5. Compute the field: $E=\frac{2\times 10^{-6}}{2.78\times 10^{-12}}\approx 7.2\times 10^5\text{N/C}$.

Concept tested: Electric field of an infinite line charge

Published 10 September 2026 · How this solution was prepared and checked