Electromagnetic Induction:
Whenever the magnetic flux linked with a coil (or a closed circuit) changes with time, an emf and a current are induced in the circuit. This phenomenon first observed by Faraday is called electromagnetic induction.
Magnetic flux :
Magnetic flux associated with any area is given by the expression
$ \large d\phi_B = \vec{B}.\vec{ds} $
$ \large \phi_B = \int \vec{B}.\vec{ds} $
Here $\vec{B}$ is the magnetic field and $\vec{ds}$ is area element. Area is taken as a vector quantity and its direction is perpendicular to surface
Magnetic Flux associated with plane coil having N turns in a uniform magnetic field $\vec{B}$ is equal to
$ \large \phi_B = N ( \vec{B}.\vec{A} ) $
$ \large \phi_B = N B A cos\theta $
Here N is the number of turns in the loop
B = magnetic field strength
A = area of the loop
θ = angle between area vector and magnetic field.