Induced magnetic field in rings

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Discussion Overview

The discussion centers on the induced magnetic fields in two concentric conducting rings, particularly focusing on the effects of a time-alternating current in the larger ring and how it influences the magnetic field in the smaller ring. Participants explore the implications of the condition r1 >> r2 and the contributions of each ring to the overall magnetic field at the center.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions why the magnetic field generated by the smaller ring is not considered when calculating the magnetic field at the center, despite the presence of the alternating current in the larger ring.
  • Another participant suggests that the condition r1 >> r2 implies that the larger ring's effects dominate, effectively negating the contributions from the smaller ring.
  • A different participant proposes that plugging in 0 for r2 in the equations should yield results consistent with a single ring, indicating that the smaller ring's influence is minimal under the given condition.
  • One participant argues that B is proportional to I/r, suggesting that as the radius decreases, the contribution of the smaller ring to the magnetic field should be greater.
  • Another participant clarifies that in the relevant formula, r refers to the distance from the origin rather than the radius of the ring itself.

Areas of Agreement / Disagreement

Participants express differing views on the significance of the smaller ring's contribution to the magnetic field, with some asserting that it is negligible under the condition r1 >> r2, while others argue that its influence should not be dismissed entirely. The discussion remains unresolved regarding the extent to which the smaller ring affects the overall magnetic field.

Contextual Notes

The discussion highlights assumptions related to the distances involved and the definitions of variables in the equations used, which may affect the interpretation of the magnetic field contributions from each ring.

dudy
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Hello,
Say I have two concentric conducting rings, where r1 >> r2 (why is this important, btw?),
and I run a time alternating current I(1) thru the larger one.
This will create a magnetic field B (also) thru the smaller ring, which in turn will create itself a magnetic field B2 and so on.
However, when asked "What is the magnetic field in the center of the rings", the answer is always that it is the magnetic field induced by I(1).
How come the field generated by the smaller ring is not taken into account ?
 
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I would guess that is what the constraint of r1 >> r2.

Get your equations and plug in 0 for r2, and it should reduce to the equation for only one ring.

When they say r1 >> r2, it means that r1 is big enough to negate the effects of r2, kind of like how when they say the distance from a wire is much less than the length of the wire, so we can assume the field is uniform.
 
khemist said:
I would guess that is what the constraint of r1 >> r2.

Get your equations and plug in 0 for r2, and it should reduce to the equation for only one ring.

When they say r1 >> r2, it means that r1 is big enough to negate the effects of r2, kind of like how when they say the distance from a wire is much less than the length of the wire, so we can assume the field is uniform.

that was my guess aswell, but B is proportional to I/r, and so the smaller r is- the greater the ring's contribution to the field.
 
I am pretty sure that r is not the radius of the ring, but distance from the origin.
 
in this formula the ring is centered at the origin, so its the same
 

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