Question

What about the Gauss theorem is not correct?
A. it can be derived by using Coulombs’ Law
B. it is valid for conservative field obeys inverse square root law
C. Gauss theorem is not applicable in gravitation
D. (a) and (b) both

Answer 1

Hint: Gauss Law says that the net electric flux out of a closed surface is equal to the charge enclosed within the closed surface divided by the permittivity of the medium enclosed. It is formulated as the expression given below. It is valid for conservative fields and also for gravity.
Formula Used:
\[\Phi =\dfrac{{{q}_{enclosed}}}{{{\varepsilon }_{o}}}\]
\[\oint{\overrightarrow{E}\cdot \overrightarrow{ds}=}\dfrac{{{q}_{enclosed}}}{{{\varepsilon }_{o}}}\]

Complete answer:
Gauss Law says that the net electric flux out of a closed surface is equal to the charge enclosed within the closed surface divided by the permittivity of the medium enclosed. It is formulated as
\[\Phi =\dfrac{{{q}_{enclosed}}}{{{\varepsilon }_{o}}}\]
Or
\[\oint{\overrightarrow{E}\cdot \overrightarrow{ds}=}\dfrac{{{q}_{enclosed}}}{{{\varepsilon }_{o}}}\]
Gauss theorem is proved by calculating the electric flux through the entirety of a closed surface given by the Coulomb's Law and comparing it to charge enclosed within the closed surface divided by the permittivity of the medium enclosed. So, Statement A is correct.
Gauss Law is valid for conservative field obeys inverse square root law; Thus, Statement B is also correct.
Gravitational Force on a body is equal to the mass of the body multiplied by the gravitational field at that point of space. Gravitational flux is also defined and Gauss law is also valid for gravity. It states that the gravitational flux through any closed surface is directly proportional to the mass enclosed within the surface. So, State C is not correct.

Option C is the correct one.

Note:
Gauss law provides us with a rather easy way of calculating fields due to any charge distribution. For this purpose, a gaussian surface is imagined. A Gaussian surface is defined as a closed 3-dimension surface. Gauss Law can also be used to calculate the Flux and hence the field lines crossing through various surfaces a body. This law was given by Carl Friedrich Gauss in 1835.