Question

State Gauss’s law in electrostatics. Explain its importance.

Answer 1

Hint: Electrostatics is a branch of physics that studies electric charges at rest. Since classical physics, it has been known that some materials, such as amber, attract lightweight particles after rubbing. Electrostatics deals with the phenomena and properties of stationary or slow-moving electric charges.

Complete step by step solution:
Gauss’ Law in electrostatics defines a relationship between electric flux passing through a closed surface with the charge enclosed inside it. This law has its application in deriving the electric field due to various charged bodies of different shapes and sizes. Electric field due to a uniformly thin charged spherical shell at a point outside it can be derived by drawing a closed Gaussian surface passing through this point.
The main formula for Gauss’s law is
 $ E\oint {ds = \dfrac{{{Q_{enclosed}}}}{{{\varepsilon _o}}}} $
Gauss Law is a basic law which is applicable for all closed surfaces. It is an important law because it allows the assessment of the amount of enclosed electric charge. It also does the mapping of the field on a surface outside the charge distribution. For all the geometries with proper symmetry, it simplifies the calculation of the electric field.
Gauss law is used to quickly find electric fields due to various arrangements like a charged sheet, thin infinite straight charged wire, etc. It comes handy to find fields in cases where symmetry is strongly present.

Note:
The electric field inside the uniformly charged thin sphere is zero. The reason for this is that if we draw a Gaussian surface inside the shell, there will be no charge enclosed inside it due to which the electric field inside it will also be zero. Thus, this also proves that if a charge is given to a thin spherical shell, all of the charge will come out and will spread uniformly on the outer surface of the shell.