Question

find the expression for electric field at a point distance r from a point charge q by using Gauss law

Answer 1

Given that

Point Charge = q

Distance = r

Electric Field = E = ? ( Using Gauss Law )

First we are going to have look at Coulomb's Law

$E = \frac{q}{4\pi \epsilon_{o}}\frac{e_{r} }{r^{2} }$

Where

e = Unit Vector giving the Direction of r

ε₀ = Electric Constant

Using this expression, we can find the expression for Electric Field at "r" by using Gauss Law.

The expression is

$\Delta.E=\frac{\rho.r}{\epsilon_{o} }$

Δ.E =  ρ.r/ε₀

It is a differential form of Gauss Law for electric field by a point charge 'q' at a distance 'r'.