Question

Define Gauss's law............​

Answer 1

Answer:

According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface

$</p><p>\oint{\vec{E}.\vec{d}s=\frac{1}{{{\in }_{0}}}q}$

For example, A point charge q is placed inside a cube of edge ‘a’. Now as per the Gauss law, the flux through each face of the cube is

$q/6ε0$

The electric field is the basic concept to know about electricity. Generally, the electric field of the surface is calculated by applying Coulomb’s law, but to calculate the electric field distribution in a closed surface, we need to understand the concept of Gauss law. It explains about the electric charge enclosed in a closed or the electric charge present in the enclosed closed surface.

As per the Gauss theorem, the total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. Therefore, If ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is;

$Q = ϕ ϵ0$

Where,

Q = total charge within the given surface,

ε0 = the electric constant.

The net flux through a closed surface is directly proportional to the net charge in the volume enclosed by the closed surface.

$Φ = → E.d → A = qnet/ε0$

the Gauss theorem relates the ‘flow’ of electric field lines (flux) to the charges within the enclosed surface. If there are no charges enclosed by a surface, then the net electric flux remains zero.

This means that the number of electric field lines entering the surface is equal to the field lines leaving the surface.

In the case of a charged ring of radius R on its axis at a distance x from the centre of the ring. E=

$4π∈01(R2+x2)3/2qx. At the centre, x = 0 and E = 0.$

In case of an infinite line of charge, at a distance ‘r’.

$E = (1/4 × πrε0) (2π/r) = λ/2πrε0. Where λ is the linear charge density.$