Two coils ‘1’ and ‘2’ are placed close to each other as shown in the figure. Find the direction of induced current in coil ‘1’ in each of the following situations, justifying your answers: (a) Coil ‘2’ is moving towards coil ‘1’. (b) Coil ‘2’ is moving away from coil ‘1’. (c) The resistance connected with coil ‘2’ is increased keeping both the coils stationary.
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Always apply Lenz’s Law: the induced current in a coil will oppose the change in magnetic flux. Approaching magnets or increasing currents lead to opposing induced fields; receding magnets or decreasing currents lead to supporting induced fields.
Lenz's law states: the direction of any induced current is such that the magnetic field it creates opposes the change in magnetic flux that produced it. In words: induced currents oppose the cause (approach, withdrawal, increase/decrease of current) of flux change.
2. How to find direction — use the right-hand rule
Procedure: (i) decide whether the magnetic flux through coil 1 is increasing or decreasing and in which direction, (ii) use Lenz's law to decide whether coil 1 must make a field that opposes (or supports) that flux change, (iii) apply the right-hand grip rule: curl your fingers in the direction of the required coil current and your thumb gives the direction of the magnetic field produced by that current.
3. Case (a): coil 2 moves towards coil 1
— When coil 2 approaches, the magnetic flux through coil 1 due to coil 2 increases (the field lines from coil 2 cut more turns of coil 1).
— By Lenz's law, coil 1 will produce a magnetic field that opposes this increase. That means coil 1 will create a field that repels the incoming field from coil 2 (i.e. opposite in direction to the increasing field).
— Using the right-hand rule, the direction of current in coil 1 that produces this opposing field is anticlockwise (as seen in the figure). Thus the induced current in coil 1 is anticlockwise.
4. Case (b): coil 2 moves away from coil 1
— When coil 2 moves away, the magnetic flux through coil 1 due to coil 2 decreases.
— By Lenz's law, coil 1 will try to oppose the decrease — it will attempt to maintain the original field by producing a magnetic field in the same direction as the original field from coil 2.
— The direction of current in coil 1 required to produce that field (same direction as coil 2's original field) is the opposite to the current found in (a). Therefore the induced current in coil 1 is clockwise (as seen in the figure).
5. Case (c): resistance of coil 2 is increased (coils stationary)
— Increasing the resistance in coil 2 reduces the current in coil 2, so the magnetic field produced by coil 2 falls (flux through coil 1 decreases).
— By Lenz's law, coil 1 will try to oppose the fall in flux by producing a magnetic field in the same direction as the original coil-2 field (to “hold up” the flux).
— Therefore the induced current in coil 1 flows in the same direction as coil 2's original current (i.e. the same direction that produced the original field). If you compare with parts (a) and (b), this direction is the same direction as in case (b) where coil 2 moved away (because both involve a net decrease of flux through coil 1).
6. Quick checklist to solve similar problems
1. Decide whether flux through the second coil is increasing or decreasing.
2. Use Lenz's law: induced field opposes change (opposes increase; supports decrease).
3. Use the right-hand rule to convert the required induced field direction into the sense (clockwise/anticlockwise) of induced current.
