Question

Consider the integral form of the Gauss's law in electrostatics:
$\oint \oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0}$
Which of the following statements are correct?

• A. It contains law of Coulomb
• B. It contains superposition principle.
• C. An elementary patch on the enclosing surface is a polar vector.
• D. An elementary patch on the enclosing surface is a pseudo-vector

Hint:

Gauss’s law is a powerful tool in electrostatics, relating the electric flux through a closed surface to the enclosed charge. It is a generalization of Coulomb’s law.

Answer 1

The Correct Option is A, B, C

1. Step 1: Gauss’s law relates the electric flux through a closed surface to the total charge enclosed by the surface. It is a generalization of Coulomb’s law.
2. Step 2: Coulomb’s law describes the force between two point charges, which can be derived from Gauss’s law. Therefore, Gauss’s law inherently includes Coulomb’s law.
3. Step 3: The superposition principle is not directly mentioned in Gauss’s law; it is related to how electric fields combine, but it is not explicitly stated in the integral form of Gauss’s law.
4. Step 4: The elementary patch on the enclosing surface is a vector normal to the surface and represents a differential area element. It is not a polar or pseudo-vector; hence, statements $3$ and $4$ are incorrect.

Conclusion: Gauss’s law provides a generalized framework that inherently includes Coulomb’s law but does not explicitly involve the superposition principle or describe the nature of the area vector as a polar or pseudo-vector.