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Below is the given question:-

My attempt- Now since the charged particle is moving it induces a magnetic field in the vicinity of the loop. So as per Lenz's Law there would be an emf induced in the loop so current would be induced having clockwise direction. But the book says the answer is option (2) I'm not able to understand this. I would like to know where I went wrong and the correct answer.

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  • $\begingroup$ Hint: figuring out induced current. directionality requires an analysis in three dimensions. $\endgroup$ – docscience Jan 12 '17 at 17:39
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Imagine the wire is infinitely long, at first. In that context it's easy to see that when the particle is far, far away from the loop, it will have practically no influence over it (i.e. the magnetic field induced by the movement of that charged particle, which is infinitely far away from the loop, wouldn't induce any current on it).

The same reasoning would work the other way around: when the particle is moving near the loop, the induced magnetic field will induce a current on the loop.

So whether the wire is infinite or not, the result is the same: as the particle approaches the loop, the influence over it increases; when it moves away from it, it decreases.

This leads to two cases:

  • When the particle moves from $A$ to the center of the wire, the magnetic field is increasing. By the right-hand rule, on the surface of the loop the magnetic field will have a direction towards you (going out of the paper). As it is increasing, by Lenz's law a current opposed to this change has to appear: the current in the loop is clockwise.
  • When the particle moves away from the loop (towards $B$), the magnetic field is decreasing. The direction is still the same (the particle keeps moving in the same direction). But now, by Lenz's law, the current on the loop must be counterclockwise.

Notice that the direction of the magnetic field is the same in both cases. It is its derivative that changes the sign, leading to the change in the direction of the current on the loop.

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To determine the direction of induced current :

  1. Decide the direction of external Magnetic field
  2. Determine whether flux is increasing or decreasing as you are causing any movement.
  3. If flux increases, current induces in a direction such that its induced magnetic field opposes the external field and vice versa. Hope This Helps. Vote me if you were satisfied...!!
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