Current density relates with electric field as
$J=\sigma \, E=\frac {E}{p}i$
where $\sigma$ =conductivity and p= resistivity or specific resistance of substance.
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.