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

Correct Answer: 2

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, \( x = 2 \).