If _SE.dS=0 over a surface, then: - Vidyadip

MCQ

If $\int_\text{S}\text{E.dS}=0$ over a surface, then:

A
The electric field inside the surface and on it is zero.
B
The electric field inside the surface is necessarily uniform.
C
The number of flux lines entering the surface must be equal to the number of flux lines leaving it.
D
All charges must necessarily be outside the surface.

✓

Answer

The number of flux lines entering the surface must be equal to the number of flux lines leaving it.
All charges must necessarily be outside the surface.

Given,

$\int_\text{s}\text{E.dS}=0$

It means the algebraic sum of number of flux lines entering the surface and number of flux lines leaving the surface.

Now, from Gauss' law,

$\int_\text{S}\text{E.dS}=\frac{\text{q}}{\in_0}$

Where q is charge enclosed by the surface.

Now,

$\int_\text{s}\text{E.dS}=0$

q = 0 i.e., net charge enclosed by the surface must be zero.

Hence, all other charges must necessarily be outside the surface.

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