`(i)` Use Gauss's 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 eries combination of two capacitors `C_(1)` and `C_(2)` with their capacitances in the ratio `1 : 2` so that the energy stored in the two of two capacitors `C_(1)` and `C_(2)` with their capacitances in the ratio `1 : 2` so that the energy stored in the two cases becomes the same.

Explanation

`(i)` N/A
`(ii)` Let the two capacitors be `C` and `2C`. In series their net capacitance be `(2C)/(3)`.
Let `V_(1)` be the p.d. applied
Energy `=(1)/(2)((2C)/(3))V_(1)^(2)` …….`(i)`
When the capacitors are in parallel net capacitance `=3C`
Energy `=(1)/(2)(3C)V_(2)^(2)`.......`(ii)`
But `(i)=(ii)`
`implies((2C)/(3))V_(1)^(2)=(3C)V_(2)^(2)`, `(V_(1)^(2))/(V_(2)^(2))=(3C)/(2C)xx3=9 : 2`
`(V_(1))/(V_(2))=(3)/(sqrt(2))`
So, `3 : sqrt(2)`