Answer the following:
`(i)` Use Gauss' law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?
`(ii)` Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors `C_(1)` and `C_(2)` with their capacitance in the ratio `1 : 2` so that the energy stored in the two cases becomes the same.

Explanation

### Step-by-Step Solution

#### Part (i): Electric Field Due to a Uniformly Charged Infinite Plane Sheet

1. **Consider the Infinite Plane Sheet**:
- Let’s assume we have an infinite plane sheet with a uniform positive charge density, denoted as \( \sigma \).

2. **Choose a Gaussian Surface**:
...