Induced magnetic field in rings

[dudy]

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 ?

 

[khemist]

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.

 

[dudy]

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.

 

[khemist]

I am pretty sure that r is not the radius of the ring, but distance from the origin.

 

[dudy]

in this formula the ring is centered at the origin, so its the same