Gauss law for magnetism on electromagnetic wave

Question

While studying electromagnetic waves, I'm confused with Gauss law for magnetism.

Shouldn't magnetic flux be zero in shown surface? Or do I understand it wrong?

Edited image after Mauricio's answer

Answer 1

The lines on your picture are not magnetic field lines. They are lines (with arrows) to represent the direction and strength of the magnetic field at each point along the z-axis at a fixed time.

The wave in your picture has a form something like $$ {\bf B} = B_0 \sin (kz - \omega t) \hat{\bf j}\ ,$$ where $\hat{\bf j}$ is a unit vector along the y-axis.

The divergence of this field $$ \nabla \cdot {\bf B} = \frac{\partial B_x}{\partial x} + \frac{\partial B_y}{\partial y} + \frac{\partial B_z}{\partial z} = 0\ .$$ Then, by Gauss's theorem, we know that $$\oint \nabla \cdot {\bf B}\ dV = \oint {\bf B}\cdot d{\bf A} = 0\ $$ and thus "Gauss's law for magnetism" (a.k.a. the solenoidal law or no monopole law) is satisfied.

This is true for any surface including the ones you have attempted to draw.

Answer 2

Gauss' law for magnetism says that there must be zero net flux about a closed surface, the picture seems to indicate the flux through an open surface.