‘Gauss’s law is based on the inverse-squaredependence on distance contained in the Coulomb’slaw.’ Explain

Gauss's Law and Coulomb's Law are both fundamental laws in electromagnetism, and they are indeed related.

1. Coulomb's Law: This law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This is where the inverse-square dependence on distance comes from. The force decreases with the square of the distance.

2. Gauss's Law: This law, on the other hand, is a way to relate the electric fields at points on a 'Gaussian surface' (an imaginary closed surface) to the total charge enclosed by that surface. It states that the electric flux through any closed surface is equal to 1/ε times the net electric charge enclosed by that surface.

3. The Connection: Gauss's Law is essentially a more general form of Coulomb's Law. It's derived from Coulomb's Law and takes into account the contribution of all charges, not just a single one. The inverse-square dependence on distance in Coulomb's Law is reflected in Gauss's Law in the way the electric field decreases as we move away from the charges (since the field lines spread out over a larger area, the field strength decreases).

So, in summary, Gauss's Law is based on the inverse-square dependence on distance contained in Coulomb's Law because it's a generalization of Coulomb's Law that takes into account the contribution of all charges, not just a single one. The inverse-square dependence is reflected in the way the electric field strength decreases as we move away from the charges.