Which of the following statements is not true about Gauss's law?

Gauss's law is not much useful in calculating electrostatic field when the system has some symmetry.

Gauss's law is indeed very useful in calculating the electrostatic field, particularly when the system has some symmetry, such as spherical, cylindrical, or planar symmetry. This makes the calculation easier as compared to direct integration using Coulomb's law. Gauss's law states that the flux of the electric field through any closed surface is directly proportional to the total charge enclosed within that surface. This law holds true for any closed surface, and the term 'q' on the right-hand side refers to the sum of all charges enclosed by that surface.

Explanation:

Gauss's law, mathematically given as ∮ E . dA = q / ε₀, is often used to simplify calculations in electrostatics when there is symmetry in the charge distribution. By choosing an appropriate Gaussian surface, such as a sphere in the case of a point charge, the electric field can be easily calculated using this law.

For example, in the case of a spherical charge distribution, the electric field at any point outside the distribution is the same as if all the charge were concentrated at the center. This is an application of Gauss's law where the Gaussian surface is chosen to match the symmetry of the problem.

Gauss's law is closely related to Coulomb's law, as it reflects the inverse square dependence of the electric field on distance, just like Coulomb's law. Any deviation from Gauss's law would indicate a violation of this inverse square law, signaling that the electrostatic system is not behaving as expected according to classical electrostatics.