1. 3. Gauss’s law
Gauss’s law is a direct consequence of Coulomb’s law, it is more convenient for calculating the electric fields of highly symmetric charge distributions and makes it possible to deal with complicated problems using qualitative reasoning.

3. Θ=0°
Θ=90°
Θ=60°
Φ=EA
Φ=0
Φ=EA cosΘ

10. Gauss’s law always holds no matter how the charge is distributed inside the closed surface and no matter is the shape of this closed surface. But Gauss’s law will not help you very much if you don’t have a situation where charges are distributed in a very symmetric way. Walter Lewin

13. The electric fields due to two oppositely charged planes
The electric fields due to the two planes cancel to give a field of zero -σ +σ
σ/2ε0
E= σ/ε0
E= 0
The electric fields due to the two planes add in the region between the planes, resulting in a uniform field of
This method is a practical way to achieve uniform electric fields with finite-sized planes placed close to each other.