How Does Induced Current Vary in a Metal Coil Within a Magnetic Field?

[Dousin12]

Homework Statement

The figure shows a metal coil labored as A. Heading torwards a region where a uniform static magnet field exists, poiting torwards the ground (hence X). The coil moves with the same constant velocity. As it enter the magnet field the coil will have an induced current in it. After a while A leaves the magnet field. Draw a I-T graph showing this scenario.

Homework Equations

[/B]
e=-d(phi)/dt might help but not sure if any equations will help

The Attempt at a Solution

My thoughts. When the coil enter the magnetic field, there will be an induced current that is counterclockwise. When it leaves the magnetic field there will be an induced current that is clockwise. Inbetween there is no current, or is it just constant inbetween? My guess would be that the current is 0 when it dosent leave or enter the magnetic field but I don't know.

So to my questions:

1. How should i know whether the graph should be constant or linear?
2. Is the current counterclockwise a.k.a negative when it enters and clockwise a.k.a positive when it leaves?
3. Is the current 0 inbetween or not?

 

[TSny]

Hello.

We don't have the figure, so we can't see the shape of the coil. Is it rectangular, circular, or something else? This is relevant to your question 1.

I believe you have the correct directions for the current when the coil is entering and leaving the field (based on your mentioning the field is represented by X's in the figure).

For question 3, think about whether or not the flux through the coil is changing once it is completely inside the field region.

 

[Dousin12]

http://imgur.com/a/czmiF

Yes the FLux is not changing when its inside, hence the current should be 0?

How about question 2 and how should i start the graph?

 

[TSny]

http://imgur.com/a/czmiF

OK, the coil is a square. This shape of the coil implies that as the coil enters the field, the flux increases at a constant rate until the coil is completely inside. So, this should help in deciding how the induced emf changes with time (or maybe doesn't change with time) as the coil enters the field.

Yes the FLux is not changing when its inside, hence the current should be 0?

Right, the flux through the coil is not changing once the coil is completely inside. Can you fill in the argument for why this implies that the current should be zero?

How about question 2 and how should i start the graph?

Once you decide how the emf depends on time, you should be able to see how the current depends on time and draw the graph.

 

[Dousin12]

1. Seriously i don't know if emf is constant or changes. I haven't learned tbh. SO i don't know if emf is linear or not etc...

2. The I is 0 coz the flux dosent change thus the emf is 0 and that means no current? Or is there a better way to explain why I is 0 inbetween?

3. So if emf is linear is I linear? If emf is just constant if I constant? I just know emf=R*I

 

[TSny]

1. Seriously i don't know if emf is constant or changes. I haven't learned tbh. SO i don't know if emf is linear or not etc...

You listed Faraday's law e = -dΦ/dt in your first post. (For a coil of N turns, this would read e = -NdΦ/dt.) This is the key equation for deciding how the emf e changes with time. I recommend that you first tsketch a graph of the flux Φ as a function of time. Let t = 0 be the time that the front edge of the coil starts to enter the field region. Due to the square shape of the coil, how does the flux increase with time? Linearly or something else?

From this graph of Φ vs t, you can then see how dΦ/dt depends on time.

2. The I is 0 coz the flux dosent change thus the emf is 0 and that means no current?

Yes, that's good.

 

[Dousin12]

Okay when i figure out graph for flux and emf. How can i find graph of I? Whats the relation between a emf and I graph.

E.g. if emf= 2*t

What would the I graph be?

 

[TSny]

Whats the relation between a emf and I graph.

Earlier you mentioned emf = IR.

 

[Dousin12]

But how can i transfer emf(t) to I(t) i see no resistance.

 

[TSny]

Since you have no numerical values for any of the quantities, I think you are only supposed to sketch the shape of the graph.

If emf and current are proportional (e = IR) then the graph of I will have the same shape as the graph of e.

 

[Dousin12]

Does the magnetic flux increase linearly when u put it in with as a square? Why is it lineraly, since the velocity is constant right? Thus the emf will be constant and thus I is constant. However, is delta flux positive or negative? This affects sign of emf? And i said in the beginning I is counterclockwise at the start, and clockwise at the end will this affect the sign of the graph?

 

[Dousin12]

So if I is constant, will I be positive or "negative" at the start? so to speak.

 

[TSny]

So if I is constant, will I be positive or "negative" at the start? so to speak.

That depend's on your sign convention for the current. You mentioned in your first post that counterclockwise current is taken to be negative.

 

[Dousin12]

But i could say counterclockwise is positive and thus the current would start at positive?

 

[TSny]

Yes. You would just need to clearly state your sign convention.

 

[Dousin12]

So this is how i think.

1. The Magnetic flux increases linerarly since A has the shape of a Square. (when A enter)
2. Inside the Flux won't change.
3. When it leaves. the flux decreases linearly

First of all. IM here very unsure if the word "increase" and "decrease" is correct in 1 and 3. Second of all. Since it has the shape of a square, is it the only reason why it would be linear or is there a more mathematical or physical way to explain why the Flux is linear here.

4. If Flux is linear. e will be a constant . And since e=R*I the I will also be constant, No R is given.
(Third of all, this sounds a bit farfetched, is it the only reason why e and I is constant)?

5. The current will be counter-clockwise at the start. Let's call that negative.
6. The current will be clockwise when it leaves. Let's call that positive. Thus the graph is something like this

Fourth of all, should i keep the "red dotted lines"
Fifth of all, is it close to a correct graph?

 

[TSny]

So this is how i think.

1. The Magnetic flux increases linerarly since A has the shape of a Square. (when A enter)
2. Inside the Flux won't change.
3. When it leaves. the flux decreases linearly

Good

First of all. IM here very unsure if the word "increase" and "decrease" is correct in 1 and 3.

Assuming you take flux into the page as positive, then it should be clear that the flux is increasing in 1 and decreasing in 3.

Second of all. Since it has the shape of a square, is it the only reason why it would be linear or is there a more mathematical or physical way to explain why the Flux is linear here.

Suppose it takes 0.6 seconds for the square to completely enter the field. Sketch pictures of the location of the square at each 0.1 second. You should be able to see that the flux increases by the same amount during each 0.1 s. Repeat for a circular shape to see a case where this is not true.

4. If Flux is linear. e will be a constant . And since e=R*I the I will also be constant, No R is given.

This is correct.

(Third of all, this sounds a bit farfetched, is it the only reason why e and I is constant)?

The reason e is constant is because the flux increases or decreases proportional to time for the square shape. The reason I is constant is I = e/R.

5. The current will be counter-clockwise at the start. Let's call that negative.

OK

6. The current will be clockwise when it leaves. Let's call that positive. Thus the graph is something like this
Fourth of all, should i keep the "red dotted lines"
Fifth of all, is it close to a correct graph?

The dotted lines are optional in my opinion, it's OK to keep them. Your graph is pretty good. You could improve it by adjusting the relative widths of the three parts to be more accurate.