Question

Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at the point $P$ is $\frac{x \sigma}{\epsilon_0}$. The value of $x$ is _________.
(All quantities are measured in SI units).

Answer 1

The electric field at $P$ is the vector sum of the fields due to the three charged sheets.

Using Gauss’s Law:

$\vec{E} = \frac{\sigma}{2\epsilon_0}$

For the point $P$:

$\vec{E}_P = \left( \frac{\sigma}{2\epsilon_0} + \frac{2\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} \right) (-\hat{i})$

Simplify:

$\vec{E}_P = \frac{4\sigma}{2\epsilon_0} (-\hat{i}) = \frac{2\sigma}{\epsilon_0} (-\hat{i})$

Thus, $x = 2$.