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.
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.
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