# Electric Flux And Gaussâ€™ Law

Electric flux density at a point *r* meters from the point charge is

Electric field intensity at a distance *r* from point charge in free space is

Gaussâ€™ Law

It states that, *total flux out of a closed surface is equal to net charge within the surface.*

**Divergence**

âˆ‡.V = . (*v*_{1}*i* + *v*_{2}*j* + *v*_{3}*k*)

Curl

Curl *V* = âˆ‡Ã— *V* =

i.e. âˆ‡Ã— V = Ã— (*v*_{1}*i* + *v*_{2 }*j *+ *v*_{3}*k*)

=

*= *

# Gradient

If V is a scalar quantity, then gradient of *v* grad *v* = âˆ‡*V*

âˆ‡V =

where, called **del operator.**

**Gaussâ€™ Divergence Theorem**

Stokeâ€™s Theorem

Maxwellâ€™s Equations in Differential (or point) Form and Integral Form

** **

# Poissonâ€™s and Laplaceâ€™s Equations

âˆ‡.âˆ‡ V = ...(1)

This equations (1) is called **Poissonâ€™s equation** for a homogeneous equation.

...(2)

This equation is called **Laplaceâ€™s equation **in rectangular coordinates and âˆ‡^{2 }is called** Laplacian** of V.