What is the Direction of Induced Current?

[max6333]

Homework Statement

The problem is simple, all I have to do is draw a voltage / time graph. The black ring is a conductor, its inner surface area is 0.01 m^2. The magnetic field points upward, B = 4T.

2. The attempt at a solution
I understand what I have to do, but I'm getting the wrong +/- sign. So I would just like a sanity check.

In the first decreasing interval, from t = 2 to t = 6. The flux is decreasing, so the magnetic field produced by the ring should be pointing upwards. Therefore the current in the ring should be counter clockwise.

If the current is counter clockwise, the voltage should be positive on the given voltmeter. However, the voltage in the solution is negative. The problem states that the voltage is positive when electrical potential is larger on the "+" side of the voltmeter.

I think it has something to do with the agreed and the actual direction of electrical current, so someone just please tell me what I am thinking wrong.

 

[SammyS]

Homework Statement

View attachment 219239
The problem is simple, all I have to do is draw a voltage / time graph. The black ring is a conductor, its inner surface area is 0.01 m^2. The magnetic field points upward, B = 4T.

2. The attempt at a solution
I understand what I have to do, but I'm getting the wrong +/- sign. So I would just like a sanity check.

In the first decreasing interval, from t = 2 to t = 6. The flux is decreasing, so the magnetic field produced by the ring should be pointing upwards. Therefore the current in the ring should be counter clockwise.

If the current is counter clockwise, the voltage should be positive on the given voltmeter. However, the voltage in the solution is negative. The problem states that the voltage is positive when electrical potential is larger on the "+" side of the voltmeter.

I think it has something to do with the agreed and the actual direction of electrical current, so someone just please tell me what I am thinking wrong.

Replace the Voltmeter with a resistor. Which end of the resistor will be at the higher potential ?

 

[TSny]

The concept of electric potential is not very useful in circuits with changing magnetic fields. For example, suppose you have the circuit shown below which consists of two voltmeters.

The positive and negative terminals of the meters are indicated by the + and - signs. There is a magnetic field in the gray area that points out of the page and is decreasing in magnitude. You can’t say that point a is at a higher (or lower) potential than point b. But that doesn’t matter. You can still tell which way the current is going to flow through each meter. It’s the direction of current through a voltmeter that determines whether the meter registers a positive or negative value.

 

[max6333]

It’s the direction of current through a voltmeter that determines whether the meter registers a positive or negative value.

I know this, the potential thing was defined in the task, not sure why. This still leaves me with the problem.
The current flows counter clockwise, right? The agreed upon direction (+ to -) is generaly used in magnetism. So this is the flow:

So shouldn't this give a positive value? The current flows from the positive to the negative.
Regarding your example,

This is the flow, so the ljeft voltmeter is negative, and the right one is positive. At least that's how I'm going about all this.
So please, tell me what's wrong here.

 

[max6333]

Update: I believe I've figured out what's wrong.
It seems that voltage is actually positive when it goes into the + pole first. The reason I thought it was opposite is this picture:

and some others, portraying the same thing.
So, in the picture, are they just using the actual direction of current (- to +) or might it be wrong? Or is there something I still have wrong?

 

[SammyS]

Update: I believe I've figured out what's wrong.
It seems that voltage is actually positive when it goes into the + pole first. The reason I thought it was opposite is this picture:
View attachment 219261
and some others, portraying the same thing.
So, in the picture, are they just using the actual direction of current (- to +) or might it be wrong? Or is there something I still have wrong?

Yes, it might just be a case of them being careless. It looks like that mistake would be easy to make for a variety of reasons.

In regards to your original analysis, I think the most important issue is that you did get the correct direction for the induced current in the ring.

 

[max6333]

In regards to your original analysis, I think the most important issue is that you did get the correct direction for the induced current in the ring.

So all I got wrong is how voltmeters work? I usually don't look for the direction of current when figuring out voltmeters, just poles. What confused me is that the metal ring is like a power source, so electricity doesn't flow from the positive pole to the negative, but the other way around. Is this a correct depiction of the poles on this thing:

 

[TSny]

So all I got wrong is how voltmeters work?

Yes, I believe so. You got the current direction right.

I usually don't look for the direction of current when figuring out voltmeters, just poles. What confused me is that the metal ring is like a power source, so electricity doesn't flow from the positive pole to the negative, but the other way around. Is this a correct depiction of the poles on this thing:
View attachment 219270

If you want to think of the ring as the "source of emf" for the rest of the circuit (the voltmeter part), then your assignment of + and - poles for the "source" looks correct in this case. The current runs from "+ pole" to "- pole" in the voltmeter part of the circuit and it runs from "- pole" to "+ pole" inside the "source", just like a battery acting as a source (as you indicate).

But you have to be careful with this idea of treating the ring as a source of emf and assigning poles to the ring. For example, suppose you leave the ring alone but hook up the voltmeter as shown below. Would you still treat the ring as a "power source" and assign + and - poles to the ring?

 

[max6333]

But you have to be careful with this idea of treating the ring as a source of emf and assigning poles to the ring. For example, suppose you leave the ring alone but hook up the voltmeter as shown below. Would you still treat the ring as a "power source" and assign + and - poles to the ring?

Well It's still tehnicaly the same thing, right? It might not be best to treat it as a circuit, since voltmeters don't allow current flow(in theory), but I still believe it's ok to imagagine it as a battery. You can use a voltmeter to probe a battery and check it's Emf.

An alternative way I would imagine it is just ignoring the whole pole thing and just looking at the direction of current flow. Do you have some better way of putting it?

Anyway, thanks for clarifying my doubts.

 

[TSny]

Well It's still tehnicaly the same thing, right? It might not be best to treat it as a circuit, since voltmeters don't allow current flow(in theory), but I still believe it's ok to imagagine it as a battery. You can use a voltmeter to probe a battery and check it's Emf.

For the figure in post #8, there would not be any current induced in the circuit. The voltmeter would read zero. Can you see why? So, if you assigned "poles" to the ring as you did in post #7, you would get the wrong answer in this case (post #8).

An alternative way I would imagine it is just ignoring the whole pole thing and just looking at the direction of current flow.

Yes.

Do you have some better way of putting it?

No.

 

[max6333]

I'm not sure why no current would be induced, is it because the conductors now form a ring that induces an opposite current? If yes, I could represent it as 2 power sources, which negate each other. Not sure about this though.

 

[TSny]

I'm not sure why no current would be induced, is it because the conductors now form a ring that induces an opposite current?

That's one way to look at it. But you can also look at the complete circuit and see that there is no magnetic flux through the circuit. That is, there is no magnetic flux through the yellow shaded area shown below

 

[max6333]

I see, thanks for sharing this method, they don't teach it in my school. Probably because they don't teach anything and I have to google everything anyway.
This doesn't destroy my pole method though. If I saw there is no flux, I would stop right there and never get to it.
Anyway, this conversation has been really helpfull understanding this curriculum, thanks.