Question

The Gaussian surface for calculating the electric field due to a charge distribution is?
A) Any surface near the charge distribution
B) Always a spherical surface
C) A symmetrical closed surface containing the charge distribution, at every point of which electric field has a single fixed value
D) None of the given options

Answer 1

Hint: We can easily answer the given question if we have a clear understanding of Gauss’s law and the Gaussian surface. Also, we need to know the relation between the charge distribution and a surface. Then only we can conclude with the correct answer of the given question.

Complete step by step answer:
First of all let us find out about Gauss's Law.
Gauss’s Law is also known as the Gauss’s flux theorem. According to Gauss’s law the distribution of electric charge to the resulting electric field is related to each other. So, we can say that the flux of the electric field of any arbitrary closed surface is proportional to the electric charge enclosed by the surface irrespective of the charge distribution.
Now let us know about a Gaussian surface.
So, a Gaussian surface is an enclosed surface in three dimensional space through which the flux of a vector field is calculated. These vector fields are gravitational field, magnetic field and electric field.
Now, we can conclude from step one and two that the Gaussian surface for calculating the electric field due to a charge distribution is a symmetrical closed surface containing the charge distribution, at every point of which the electric field has a single fixed value.

Hence, option (C) is the correct choice of the given question.

Note: Mathematically, we can represent Gauss’s law as $\phi = \dfrac{Q}{{{\varepsilon _0}}}$ where, $Q$ is the total charge distribution over the surface and ${\varepsilon _0}$is the permittivity or electric constant. With the help of Gauss’s law we can easily calculate the electric field.