Rankers Physics

Gauss's Law: Practice Problem & Solution

Two parallel infinite line charges with linear charge densities $+\lambda \text{ C/m}$ and $-\lambda \text{ C/m}$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges? (2019)
Zero
$\frac{2\lambda}{\pi\epsilon_0 R} \text{ N/C}$
$\frac{\lambda}{\pi\epsilon_0 R} \text{ N/C}$
$\frac{\lambda}{2\pi\epsilon_0 R} \text{ N/C}$

Solution Explained:

To solve this problem, we apply the core principles of Gauss's Law. Understanding the underlying formula is key to arriving at the correct answer below:

The electric fields due to both line charges at the mid-point point in the same direction. Magnitude of field due to each line is $E = \frac{\lambda}{2\pi\epsilon_0 R}$. Total field $E_{net} = E + E = \frac{\lambda}{\pi\epsilon_0 R}$.

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