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

  1. The number of flux lines entering the surface must be equal to the number of flux lines leaving it.
  2. 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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