If some electric flux enters a cube, the same amount leaves through the other surface. Hence the net flux is zero. Why? I know the mathematical answer to this but what's the physical meaning and significance of this? Also, why does something like this not happen in a 2-d object?

Dear Student
Gauss law is behind all this. It says that surface integral of B.ds is equal to volume charge density. If there is no charge inside the cube,volume charge density will be 0 and hence the closed surface integral of B.ds which is basically Flux will be zero.

In 2D object,closed surface integral can’t be calculated ,so something like that doesn’t happen in 2D objects

Thanks