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
All charges must necessarily be outside the surface.
C
The number of flux lines entering the surface must be equal to the number of flux lines leaving it.
✓
B and c both

✓

Answer

Correct option: D.

B and c both

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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