Electric field Vector The Hub Of Electrostatics 1

[i_am_ayush]

Hey I cought out a pattern in Electrostatics and i created it in my revision notes. I have uploaded it
please Suggest if any correction required

 

[dipole]

You've written that the electric flux is given by,

$\varphi = \int\vec{E}\cdot d\vec{S}$

which is correct, but then you've written that

$\vec{E} = -\vec{\nabla} \varphi$ which is wrong! The electric field can be written as the gradient of the electric potential, not the the flux.