Two parallel infinite line charges with linear charge densities $+\lambda ext{ C/m}$ and $-\lambda ext{ C/

Question

Two parallel infinite line charges with linear charge densities $+\lambda 	ext{ C/m}$ and $-\lambda 	ext{ C/m}$ are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

Accepted Answer

The electric field due to an infinite line charge at distance $r$ is $E = \frac{\lambda}{2\pi\epsilon_0 r}$. At the mid-point (distance $R$ from each), the fields from both charges point in the same direction. $E_{total} = E_1 + E_2 = \frac{\lambda}{2\pi\epsilon_0 R} + \frac{\lambda}{2\pi\epsilon_0 R} = \frac{2\lambda}{2\pi\epsilon_0 R} = \frac{\lambda}{\pi\epsilon_0 R} 	ext{ N/C}$.

Step-by-Step Solution

Practice All PHYSICS Questions