To answer this question, we need to understand the various components of Gauss' Law in electrostatics and how it relates to the given options:
Gauss' Law in electrostatics is given by the integral form:
∮⋅d=In this equation:
is the electric field vector.
d is the differential vector element of the surface area on a closed surface.
Q is the total charge enclosed within the surface.
ε0 is the permittivity of free space.
Let's examine each option to determine which statements are correct:
Option A: It contains the law of Coulomb.
Gauss' Law is directly derived from Coulomb's law for a point charge. It states that the net electric flux through any closed surface is proportional to the charge enclosed within that surface. Therefore, this statement is correct. Gauss' Law essentially generalizes Coulomb's law to any closed surface.
Option B: It contains the superposition principle.
Gauss' Law inherently relies on the superposition principle. The total electric field due to multiple charges is the vector sum of the electric fields due to individual charges. This is because the law of superposition applies to electric fields, which are linear, allowing Gauss' Law to hold for systems with multiple charges. Hence, this statement is also correct.
Option C: An elementary patch on the enclosing surface is a polar vector.
The vector
d represents an infinitesimal area element on the surface, with the direction of the vector normal (perpendicular) to the surface. A normal vector to a surface is considered a polar vector because its properties do not change under a coordinate inversion. Therefore, this statement is correct.
Option D: An elementary patch on the enclosing surface is a pseudo-vector.
A pseudo-vector (or axial vector) is a vector that changes sign under inversion of the coordinate system (like angular momentum or magnetic field). The normal vector to a surface element does not change sign under inversion; hence, it is not a pseudo-vector but a polar vector. Thus, this statement is incorrect.
Therefore the correct statements are: Option A, Option B, and Option C.