গাউসের সূত্র (গুণগত আলোচনা)

Gauss's law is quite an important relation in the physics of electricity. Once the concept of electric flux is established (the product of the electric field and the perpendicular cross-section of the area through which it is passing) Gauss's law can be very helpful in simplifying many relations that may otherwise be tedious to solve. What Gauss's law states is that for any closed surface, the electric flux out of that object is always equal to:

$$\frac{Q}{\epsilon_0}$$

In this equation, $Q$ is the total charge enclosed by the object, and $\epsilon_0$ is the permittivity of free space, also called vacuum permittivity (a constant). Thus, for all closed regions of charge, the electric flux of that region always simplifies to this rather basic proportion, and this is what makes Gauss's law so useful in practical applications. This equation can be verified by using the integral definition of electric flux for many basic solid objects:

$$\int\vec{E} \cdot \vec{dA}$$