1. **Problem Statement:** We have two parallel, infinite conducting sheets with equal and opposite charge densities. We need to determine the correct set of equipotential surfaces for this system. 2. **Concepts and Formula:** For two infinite parallel sheets with opposite charges, the electric field between them is uniform and directed from the positively charged sheet to the negatively charged sheet. 3. **Electric Field and Equipotential Surfaces:** The electric field $\vec{E}$ is perpendicular to the sheets and constant in magnitude between them. Equipotential surfaces are always perpendicular to the electric field lines. 4. **Equipotential Surfaces for Parallel Plates:** Since the electric field is uniform and perpendicular to the plates, the equipotential surfaces are parallel planes between the sheets. 5. **Analyzing the Options:** - Option A shows alternating dashed and solid lines parallel to the sheets, which matches the expected equipotential surfaces. - Option B shows horizontal lines but also includes a line with plus signs, which is inconsistent. - Option C and D show circular or other shapes, which do not correspond to the uniform field between infinite sheets. 6. **Conclusion:** The correct set of equipotential surfaces is option A, which shows parallel lines between the sheets, consistent with the uniform electric field and perpendicular equipotential surfaces. **Final answer:** Option A