An infinitely long straight line carries a uniform linear charge density $\lambda =4\mu \text{C/m}$. Find the magnitude of the electric field at a point 3 cm away from the line.

Step-by-step solution

1. For an infinite line of charge, the electric field at radial distance $r$ is $E=\frac{lambda}{2pivarepsilo{n}_{0}r}$.
2. Convert the given values: $\lambda =4\times 10^{-6}\text{C/m}$, $r=0.03\text{m}$, ${\epsilon }_0=8.854\times 10^{-12}{\text{C}}^2/({\text{N⋅m}}^2)$.
3. Compute the denominator $2pivarepsilo{n}_{0}r=2\pi \times 8.854\times 10^{-12}\times 0.03\approx 1.6695\times 10^{-12}$.
4. Divide $\lambda$ by this value: $E=4\times 10^{-6}/1.6695\times 10^{-12}\approx 2.40\times 10^6\text{N/C}$, directed radially outward.

Concept tested: Electric field of an infinite line charge

Published 16 September 2026 · How this solution was prepared and checked