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 dictates that an induced current will generate a magnetic field that opposes the change in magnetic flux causing it. In simpler terms, induced currents counteract the action that led to the flux change (e.g., approaching, receding, current increasing/decreasing).
2. Determining Direction: The Right-Hand Rule
Procedure: (i) Assess if the magnetic flux through coil 1 is increasing or decreasing and its direction. (ii) Apply Lenz's law to determine if coil 1's induced field should oppose or support this flux change. (iii) Utilize the right-hand grip rule: point your thumb in the direction of the required magnetic field produced by the induced current, and your curled fingers will indicate the direction of that current.
3. Scenario (a): Coil 2 Approaches Coil 1
— As coil 2 moves closer, the magnetic flux through coil 1 from coil 2 intensifies (field lines from coil 2 intersect more turns of coil 1).
— According to Lenz's law, coil 1 must generate a magnetic field opposing this increase. This means coil 1 will produce a field that repels the incoming field from coil 2 (i.e., it will be in the opposite direction to the intensifying field).
— Using the right-hand rule, the current direction in coil 1 that generates this opposing field is anticlockwise (as depicted in the figure). Consequently, the induced current in coil 1 is anticlockwise.
4. Scenario (b): Coil 2 Recedes from Coil 1
— When coil 2 moves away, the magnetic flux through coil 1 due to coil 2 diminishes.
— By Lenz's law, coil 1 will attempt to counteract this decrease by generating a magnetic field in the same direction as the original field from coil 2, aiming to sustain the flux.
— The current direction in coil 1 necessary to produce this field (matching coil 2's original field direction) is the opposite of what was determined in scenario (a). Therefore, the induced current in coil 1 is clockwise (as shown in the figure).
— An increase in coil 2's resistance reduces its current, thereby weakening the magnetic field it produces and consequently decreasing the flux through coil 1.
— Per Lenz's law, coil 1 will seek to oppose this flux reduction by creating a magnetic field aligned with coil 2's original field (to "support" the flux).
— Consequently, the induced current in coil 1 flows in the same direction as coil 2's original current (i.e., the direction that generated the original field). Comparing this to scenarios (a) and (b), this direction is identical to that in case (b) where coil 2 moved away, as both scenarios involve a net decrease in flux through coil 1.
6. Quick Checklist for Similar Problems
1. Determine if the flux through the second coil is increasing or decreasing.
2. Apply Lenz's law: the induced field opposes the change (opposes an increase; supports a decrease).
3. Use the right-hand rule to translate the required direction of the induced field into the sense (clockwise/anticlockwise) of the induced current.
