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 connects electric flux through a closed surface to the enclosed total charge. It extends Coulomb's law.
2. Step 2: Coulomb's law defines the force between two point charges and can be derived from Gauss's law. Thus, Gauss's law encompasses Coulomb's law.
3. Step 3: The superposition principle isn't directly part of Gauss's law. It relates to electric field combination, but isn't explicitly stated in the integral form of Gauss's law.
4. Step 4: The area element on the enclosing surface is a vector, normal to the surface, representing a differential area. 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.