Question

what is gauss's law?explain

Answer 1

The flux passing through a closed three dimensional surface is equal to the electrostatic charge divided by ε (electric permittivity of the medium).

$\phi= \int\limits^{}_{S} {\vec{E}.\vec{dS}} \, {}=\frac{q}{\epsilon_0}$

Application:

For a point charge Q, we want to find the electric field intensity at a distance d.  

We imagine a spherical closed surface of radius d around the point charge Q (placed at the center).  Then we apply Gauss' law of electrostatics.  We find the surface integral.   From symmetry of the sphere, electric field strength E is same all around on the surface.  The angle between the surface and electric field is 0⁰ and same all over the surface.  Both point along the radius.

Φ = E * 4π d² =  Q / ε₀

     =>  E = 1/(4πε₀) * Q / d²

we know this formula already, which is derived  from Coulomb's law.