Question

Choose the INCORRECT statement: A) Gauss' law can be derived from Coulomb's law B) Gauss' law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface C) Coulomb's law can be derived from Gauss' law and symmetry D) Gauss' law applies to a closed surface of any shape E) If a closed surface encloses no charge, the electric field is zero everywhere on the surface

Answer 1

The INCORRECT statement is E) If a closed surface encloses no charge, the electric field is zero everywhere on the surface, because the presence of external charges can still result in a non-zero electric field on the surface.

Step-by-step explanation:

The question asks you to identify the INCORRECT statement among the given options regarding Gauss's law.First, let's review the statements:

A) Gauss's law can be derived from Coulomb's law.

B) Gauss's law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface.

C) Coulomb's law can be derived from Gauss's law and symmetry.

D) Gauss's law applies to a closed surface of any shape.

E) If a closed surface encloses no charge, the electric field is zero everywhere on the surface.

The incorrect statement is E)

If a closed surface encloses no charge, the electric field is zero everywhere on the surface. This is incorrect because even if the enclosed net charge is zero, the electric field on the surface can still be non-zero due to charges outside the closed surface.

Gauss's law indicates the total electric flux through a closed surface is related to the charge within, not to the electric field itself.

Answer 2

A

Step-by-step explanation:

A)

INCORRECT

No, Gauss's Law can not be derived from Coulomb's Law alone. Since, Coulomb's Law provides electric field produced by a single point charge. Therefore, it is important to assume principle of super position along with Coulomb's law to get the field due to all charges. So, Gauss's Law can be proved by the help of both Super Position Principle and Coulomb's law.

B)

CORRECT

Yes, Gauss' law states that the net number of lines crossing any closed surface in an outward direction is proportional to the net charge enclosed within the surface.

C)

CORRECT

Yes, Coulomb's law can be derived from Gauss' law and symmetry.

D)

CORRECT

Yes, Gauss's Law applies to a closed surface of any shape.

E)

CORRECT

Yes, if a closed surface encloses no charge, the electric field is zero everywhere on the surface.