State Faraday's laws of electromagnetic induction.

Explanation

Motional emf from Faraday.s law : Let us consider a rectagular conducting loop of width l in a uniform magnetic field `vecB` which is perpendicular to the plane of the loop and is directed inwards. A part of the loop is in the magnetic field while the remaining part is outside the field.
When the loop is pulled with a constant velocity `vecv` to the right the area of the portion the loop within the magnetic field will decreases. Thus , the flux linked with the loop will also decrease. According to Faraday.s law, an electric current is induced in the loop which flows in a direction so as to oppose the pull of the loop .

Let x be the length of the loop which is still within the magnetic field , then its area is lx. The magnetic flux linked with the loop is `Phi_B=int_A vecB*dvecA=BA cos theta`
Here `theta =0^@ and cos 0^@=1`
=BA
`Phi_B =Blx` ........(1)
As this magnetic flux decreases due to the movement of the loop the magnitude of the induced emf is given by
`varepsilon=(dPhi_B)/(dt) =d/(dt)(Blx)`
Here both B and l are constants. Therefore,
`varepsilon=Bl(dx)/(dt)=Blv` .......(2)
Where `v=(dx)/(dt)` is the velocity of the loop. This emf is known as motional emf since it is produced due to the movement of the loop in the magnetic field.