Imagine a situation, in which an infinite sheet with positive charge $$+\sigma$$ per unit area lies in the $$xy$$ plane and a second infinite sheet with negative charge $$-\sigma$$ per unit area lies in the $$yz$$ plane. The net electric field $$E$$ at any point $$(x,y,z)$$ that does not lie on either of these planes $$xy$$ or $$yz$$ can be expressed as

A

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

B

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

C

$$\vec E = \frac{\sigma}{2\epsilon_0}\left[-\frac{x}{\lvert x\rvert}\hat{i} + \frac{z}{\lvert z\rvert}\hat{k}\right]$$

D

$$\vec E = \frac{\sigma}{\epsilon_0}\left[\frac{x}{\lvert x\rvert}\hat{i} - \frac{z}{\lvert z\rvert}\hat{k}\right]$$