Motional E.M.F:

Consider a closed conducting loop ABCD, with the arm CD sliding, placed in a horizontal plane. Let B be a uniform magnetic field perpendicular to the plane of the loop and directed into it.

Let the conductor CD be moved towards right with a velocity v. As the conductor CD slides, the area of the closed loop changes from ABCD to ABEF, during a small interval of time dt.

The change in flux passing through the closed loop dφ.

= Flux density B x Change in area

= B x (area ABEF - ABCD)

= B x area DCEF

= B x CD x DF = Bl x vdt

Where l is the length of the conductor CD in the magnetic field.

Induced e.m.f = - , the magnitude of the induced e.m.f. = E =  = Blv.

The e.m.f. induced due to the motion of the conductor in a uniform magnetic field is called the motional e.m.f. It depends upon

(i) the magnetic flux density B;

(ii) the length of the conductor l in the magnetic field;

(iii) the speed v with which the conductor is moved in the magnetic field.

If the conductor is inclined at an angle θ with the direction of B then the magnitude of the induced emf = Blv sinθ.

The direction of the induced e.m.f. is given by Lenz's law or Fleming's right hand rule. If R is the resistance of the whole circuit then the magnitude of the induced current.