1. Field due to one infinite charged sheet

For an infinite thin plane sheet with uniform surface charge density $\sigma$, the magnitude of electric field on either side is

Direction:

• away from the sheet if $\sigma>0$
• toward the sheet if $\sigma<0$

2. Interpretation of the figure

Since the options indicate zero field in the middle region for the correct configuration, the two sheets must carry equal and opposite surface charge densities, $+\sigma$ and $-\sigma$, with regions:

• Region $I$: left of both sheets
• Region $II$: between the sheets
• Region $III$: right of both sheets

Let $\hat n$ be the unit vector from left to right.

3. Electric field in each region by superposition

Region $I$ (left of both sheets)

• Field due to left positively charged sheet: toward left, i.e. $-\dfrac{\sigma}{2\varepsilon_0}\hat n$
• Field due to right negatively charged sheet: toward the negative sheet, i.e. toward right, so $+\dfrac{\sigma}{2\varepsilon_0}\hat n$

These cancel if the left sheet is $+\sigma$ and right is $-\sigma$. But option C has nonzero outer regions and zero middle region, which corresponds to the actual figure being two sheets with same sign? Let us evaluate carefully.

If the two sheets have the same positive charge density $\sigma$:

• In Region $I$, both fields point left:

• In Region $II$, fields oppose and cancel:

• In Region $III$, both fields point right:

4. Match with options

This gives

which matches Option C.

5. Final answer

This means the two sheets in the figure must be identically charged, and the field cancels between them while adding outside.