Question

Choose the incorrect statement

• A. Gauss's law applies to a closed surface of any shape
• B. according to Gauss's law, if a closed surface encloses no charge, electric field must vanish everywhere on the surface
• C. Gauss's law can be derived from Coulomb's law
• D. according to Gauss's law, the net number of lines crossing any closed surface in an outward direction is proportional to the net charge on surface

Answer 1

Answer: (B)

According to Gauss's law, if a closed surface encloses no charge, electric field must vanish everywhere on the surface.
It is incorrect, because the field can still came from external sources, so while the integral must vanish, there can still be an electric field on the surface.
According to Gauss's law, the net number of lines crossing any closed surface in an outward direction is proportional to the net charge on surface.
$\because {\varphi }_{\text{enclosed }}=\frac{q_{\text{net }}}{{\epsilon }_0}$
$\Rightarrow {\varphi }_{\text{enclosed }}\propto q_{\text{net }}$