The magnetic flux through a surface is given by
$ \phi=\vec{B}. \vec{A} =BA\, cos \,\theta$
Now since the magnetic field $\vec{B}$ is parallel to the surface, so the magnetic flux in a direction perpendicular to the surface will be $\phi=BA\, cos \,90^{\circ}=0$
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
When we place the conductor in a changing magnetic field.
When the conductor constantly moves in a stationary field.