The direction of induced current may be found by Flemming’s right hand rule and Lenz’s law.
Flemming’s right hand rule is applicable for dynamically induced emf and Lenz’s law is applicable for statically induced emf.

FLEMMING’S RIGHT HAND RULE: As per rule, if the Thumb, First finger and Second finger makes 90° angle between each other, the Thumb indicates the motion of conductor relative to magnetic field, the first finger indicates the direction of magnetic field and the second finger indicates the direction of induced current within the conductor.

LENZ’S LAW: It states that electromagnetically induced current always flows in a closed path in such a direction that the magnetic field, produced by the current will oppose the change that produce the current. That is it opposes the very cause which produce the current.

EXPLANATION: At the year 1834, a Russian physicist Heinrich Friedrich Emil Lenz (1804-65) states that when a permanent magnet moves towards a coil, it induces an electric current through the coil which increases the magnetic flux surrounding coil, the direction of induced current is such that it opposes the increasing magnetic flux.

Suppose an N pole permanent magnet moves towards a coil, as per Faraday’s laws of electromagnetic induction, a current induce through the coil which also create its own magnetic field. Now as per Lenz’s law this created magnetic field opposes the increasing flux through the coil. That means the side of coil near magnet acts as N pole and as we know, like pole repeal each other, some mechanical energy is required for overcoming this repulsive force, converted into electric energy which shows at galvanometer.

Again, when permanent magnet moves away from the coil, the same coil side acts as S pole and so here also some mechanical energy required for overcoming the attractive forces as unlike pole attract each other which shows in the form of electric energy indicated at galvanometer in opposite direction.

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