Question

If $∮_s\overrightarrow{E}.\overrightarrow{dS}=0$ over a surface, then:

• A. the electric field inside the surface is necessarily uniform
• B. the number of flux lines entering the surface must be equal to the number of flux lines leaving it
• C. the magnitude of electric field on the surface is constant
• D. all the charges must necessarily be inside the surface

Answer 1

Answer: (B)

the number of flux lines entering the surface must be equal to the number of flux lines leaving it

Answer 2

The correct option is (B): the number of flux lines entering the surface must be equal to the number of flux lines leaving it

$\oint\vec{E}.\vec{d}s$ represents electric flux over the closed surface.

When $\oint\vec{E}.\vec{d}s$=0, it means the number of flux lines entering the surface, will be equal to the number of flux lines leaving it.

As, $\oint\vec{E}.\vec{d}s=\frac{q}{\epsilon_0}$ where q is the charge enclosed by the surface.

When $\oint\vec{E}.\vec{d}s=0$,q=0 i.e, net charge enclosed by the surface must be zero.