Lenz's law

[u/Sorry_Initiative_450]

The loop is placed in a uniform magnetic field pointing into the page, and the field is increasing over time. Which way would the induced current flow?(The answer should be in the direction I showed in the image). What confuses me is, a smaller loop creates a stronger magnetic field per amp, so why does the current flow along the outer circumference to oppose the change, while the inner circumference ends up reinforcing the increasing field instead of opposing it?

[u/Azazeldaprinceofwar]

Because there is no “outer loop” and “inner loop” like you’re thinking, the outer and inner circles don’t close. If that did they’d both run counterclockwise for the reason you indicated. Here however you just have one very weird loop and it, as expected, runs counterclockwise such as to resist the change in flux through the loop (ie in the band between the circles)

[u/Sorry_Initiative_450 → u/Azazeldaprinceofwar]

But the inner part does in fact create a magnetic field which is along the same direction as the external field, so doesn't that do the opposite of what lenz's law says? The outer part too creates a magnetic field that opposes the external field but the magnitude of the field due to the inner part should be greater, so essentially the net magnetic field due to this loop will be along the external field.

[u/basketas87 → u/Sorry_Initiative_450]

But the outer loop is bigger so it affects "more" of the extermal magnetic field. It's a weird way to look at it anyway. Mathematically, Lenz's law is just represended as a minus sign in the Faraday law U=-d(B*S)/dt, and in a more complicated geometry like this it is probably not good to look at it in it's simplified form stating the induced magnetic field has to oppose the change. It still does, however, but it's not necessarily immediately obvious.

You can also look at it a different way. The "inside" of the small loop is stricktly speaking the outside of the very distorted closed loop. Inside the closed loop, the induced magnetic field always opposes the external change.

[u/Sorry_Initiative_450 → u/basketas87]

it is probably not good to look at it in it's simplified form stating the induced magnetic field has to oppose the change.

Right, I do get it mathematically. It is just that when I think of it like you mentioned, it gets confusing.

[u/Flob368 → u/Sorry_Initiative_450]

Don't think of the inside of the inner loop at all.
The space between the two rings, that's your inside. That's the only thing you have to care about. And its perimeter has a direction. That's all you need to think about.

[u/Warshrimp → u/Azazeldaprinceofwar]

But if the gap is light years away how could a local particle know what it is encountering?

[u/Azazeldaprinceofwar → u/Warshrimp]

It wouldn’t. Locally the moment the magnetic field turns on both circles try circulate counterclockwise, but this would result is a charge build up and electrostatic forces are very strong so very quickly (a few milliseconds) the system will reach a steady state in which current flows uniformly throughout the loop. So you can think of it like this, both circles try to circulation counterclockwise electrostatically resist each other for a moment then the outer loop wins and so current flows the opposite direction through the inner circle despite magnetic forces pushing current the other way due to electrostatic pressure from current in the outer circle pushing it through.

[u/Cheticus]

They're not independent loops, it's one loop. The flux is increasing through the loop, and so Lenz's law says that there is an EMF developed which creates a field to oppose that increasing flow.

Start from a single circular loop with a small little divot in the inside of it, and then keep making the divot bigger until you approach your image. Why should the direction of current reverse when the flux direction is constant through the loop?

*I am not an electrical engineer or good at physics and am probably wrong

[u/FreeH0ngK0ng_]

Haven't done EM in ages but I think

B field for a wire loop as such goes like 1/r

A for a circle goes like r²

So magnetic flux Φ=BA generated by each loop goes like r

So this arrangement generates a net flux that is pointing out of the paper (sorry for poor English as flux should be a scalar), which is one that resists change in B

Also current along vertical parts do not contribute

[u/Send-More-Coffee]

Okay, the field is uniform into the page right? I'm going to explain why we can ignore all of the field except the part contained by the inner loop, by analogy.

Let's imagine that this is gravity. You're standing on the surface of the earth. The earth in front of you (at a downward angle) is not pulling towards the center of the earth. It's pulling you towards it. Similarly the earth behind you, at the same downward angle is pulling you towards it. These forces cancel out and produce a net force downward.

Because this is a perfect circle (excluding the gap, which I'm going to assume is negligible) we can ignore the field outside the inner circle because every point will have a reflected opposite point that would induce the current to flow in the opposite direction. Just like how the earth in front of you is canceled out by the dirt behind you.

Now, why can't we do that for the inner loop as well? Because unlike every other point on the page, a reflection here does not change the direction of flow in the loops. Why? As you know, the force exerted by a magnetic field drops as the distance to the source increases. So because the inner loop is always going to be closer to this part of the magnetic field, there is a non-symmetrical force imposed on the electrons in the wires. This asymmetry means the inner wire wins the shoving match between the two induced currents and the current flows as in the diagram.

Hope this helps.

In fact, I believe it's legitimate to simplify the problem to "There's a magnetic field going into the page at the center of the circle. What direction is the current in the wire flowing".

Edit: Upon closer reading of your confusion, you're correct. This is an inefficient direction for the current to be flowing and it is resisting the magnetic field. The NET current is as depicted, but the B field is inducing a current as per the right hand rule , in the outer as the inner wire. However, remember that the force drops by the inverse of the radius. So as the distance between the inner- and outer-wires increases, the inefficiency of this layout decreases as well.

[u/Appropriate_View8753]

That's a curved bar, not a loop.