Question

Suppose the flux of electric feild is zero accross a closed surface then,

• A. electric feild must be zero every where
• B. charge inside the surface must be zero
• C. charge may be present inside the surface
• D. electric field may be zero at every point on the surface

Answer 1

Answer: (C), (D)

The correct options are
C charge may be present inside the surface
D electric field may be zero at every point on the surface

Given that flux of electric field is zero across a closed surface.

So, flux is $\varphi =E.A$

$E=$ electric field across surface

$A=$ area of closed surface

Since $A\ne 0$

means, when $\varphi =0$ implies $E=0$ ...(i)

Also, from Gauss Theorem, flux through a closed surface $\varphi =\frac{q}{{\epsilon }_0}=\oint \overrightarrow{E}.\overrightarrow{dS}$

$q=$ charge (total) enclosed in the closed surface

$\overrightarrow{dS}=$ area element on the surface

If $\varphi =0\Rightarrow$ net charge within the surface is zero. ...(ii)

But charge may be present in the surface.

So, when $\varphi =0$, from (i) and (ii) we see that charge may be present or electric field may be zero.