Question

State Gauss’s law in electrostatics.

Answer 1

Hint : In electrostatics, Gauss law plays an important role. It is helpful in those problems where we can construct an imaginary surface to find the electric field. As electric flux gives the intensity of electric field.

Complete step by step solution: If Q is the net charge enclosed by a surface and ${\varepsilon _0}$ is the permittivity of the vacuum, then scientist Gauss found that the electric flux through that closed surface will become-
$\phi = \dfrac{Q}{{{\varepsilon _0}}}$
Hence, Gauss states that in electrostatics the total electric flux through a closed surface is always equal to the ratio of the net charge enclosed by the surface and the permittivity of the vacuum.
The integral formula of the Gauss law is-
\[\phi = \oint\limits_S {\overrightarrow E } .\overrightarrow {ds} = \dfrac{Q}{{{\varepsilon _0}}}\]
Here $\oint\limits_S {} $ is the surface integral of that closed surface.

Additional Information: Gauss law is a very important law of electrostatics. Some important applications are-
1. Gauss law can be helpful in those problems where an imaginary closed surface can be constructed to calculate the electric field. This imaginary surface is known as Gaussian surface.
2. Gauss law can be used for all types of closed surfaces having different shapes and sizes.
3. If symmetry can be made in any problem then Gauss law makes the problem more easier and the integral part will be solved easily.

Note: We have to remember that in electrostatics the charge is motionless. We have to keep in mind that electric flux gives the intensity of the electric field. The permittivity which is taken in the Gauss formula is always the permittivity of the vacuum.