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

The Correct Option is B

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.