According to Lenz's principle, induced emf in a circuit opposes the cause due to which it was induced.
Consider the following examples.
(a) Suppose that the north-pole of a bar magnet is moved towards a conducting wire loop as shown in the figure. Due to a modification in the magnetic flux associated with the loop, a current is follow. Due to induced current, a magnetic force is provided and this magnetic field opposes the motion of bar magnet. The direction of the produced current can be deduced by the following argument: the north pole is moving towards the loop; therefore to oppose the motion of the bar magnet only a north pole will be induced on that face of the loop which faces the magnet.
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(b) A rectangular loop ABCD is being pulled out of the magnetic field which is directed into the plane of the paper. Perpendicular to the field of the surface. As the loop is gone out of the field, the flux added with the loop decreases. The produced current flows in the loop in a sense so as to oppose the decrease in this flux. For that is occurring the magnetic field due to the induced current in the loop must be directed into the plane of the paper. Thus the current in the loop have to flow be clockwise.
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Induced emf because of motion of a conductor in magnetic field
Suppose a conductor is moving with velocity V in a uniform magnetic field B . We provide a small component PQ = dl of the conductor, then induced e.m.f. in the component.
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Where θ is the angle in between B and v and a is the a angle between element and direction of force
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