Induced Current - is there one if inside constant B field?

[skibum143]

Homework Statement

A box of wire is moving within a constant B field. Is there an induced current?

Homework Equations

Slap rule

The Attempt at a Solution

Since the wire is experiencing constant B field, how would we figure out whether or not there is a current? I know there is a current if the B field is changing (Faradday's law) but if it is in a constant B field, I don't think there would be a current?

 

[collinsmark]

Hello skibum143,

You know that Faradday's law involves changing magnetic flux, and flux involves area. The wire is sweeping out an area per unit time. I.e., the area in this case is a function of time. And flux is a function of area. That fact can help you with this problem.

 

[skibum143]

But the area exposed to the magnetic field isn't changing, so area is constant. So flux isn't changing, so Emf isn't changing, does that mean there isn't a current?

 

[collinsmark]

But the area exposed to the magnetic field isn't changing, so area is constant. So flux isn't changing, so Emf isn't changing, does that mean there isn't a current?

I can't give you the answer. But I can say, even though the area of the box itself is not changing as a function of time, the area swept out by the box of wire is changing as a function of time.

 

[skibum143]

I know you can't give answers, sorry, I just don't understand. I don't know what the "area swept out" means, because the magnetic field is constant, so shouldn't that be constant instead of changing?

Here is what I don't get: either way the current runs, (with a B field into the page) it will all point into the box (clockwise) or out of the box (counterclockwise current) - so there wouldn't really be a force on the box in any direction, so how would you know whether or not there is a current?

 

[collinsmark]

I know you can't give answers, sorry, I just don't understand. I don't know what the "area swept out" means, because the magnetic field is constant, so shouldn't that be constant instead of changing?

Here is what I don't get: either way the current runs, (with a B field into the page) it will all point into the box (clockwise) or out of the box (counterclockwise current) - so there wouldn't really be a force on the box in any direction, so how would you know whether or not there is a current?

I admit to making a few assumptions earlier, which may or may not apply to this problem. Much of what I wrote earlier assumes that this "box" of wire has some sort of 3 dimensional configuration (as opposed to a "square" etc), such that some of the wires might be on the outside of the uniform magnetic field.

To get to bottom of it, (I'm not sure if your problem had more information to it like a figure or something), You might want to consider the induced emf in each line of wire in the box (if any). Then decide, based on the configuration, whether or not any current loops could form.

 

[skibum143]

I know the EMF is zero when the wire box is in the constant square magnetic field, that is why I assumed current is zero. I just don't really know how to prove it, other than there is no change in magnetic field, so there is no induced current. That seems to make sense.

 

[collinsmark]

I know the EMF is zero when the wire box is in the constant square magnetic field, that is why I assumed current is zero. I just don't really know how to prove it, other than there is no change in magnetic field, so there is no induced current. That seems to make sense.

The current may very well be zero, depending on the configuration. (But without more details, I can't say that with certainty without seeing a diagram or something).

But if you wish to prove it, you might want to describe the induced emf on each wire in the box. Generally speaking, emf (aka voltage) is produced over a wire as it moves through a constant magnetic field. But depending on the configuration, it could be that the combined emf of any possible current loop adds up to zero (i.e. the emf of one wire completely opposes that of another wire, etc., so that there is no net emf in the loop, and no current flows).

 

[skibum143]

Sorry, I should have scanned the problem earlier...I attached it here - can you see if it makes more sense to you now? Thanks!

The only part I don't understand is the current on the middle block (and hence, the force on the middle block). I get the first and third parts.

Thanks!

 

[collinsmark]

Sorry, I should have scanned the problem earlier...I attached it here - can you see if it makes more sense to you now? Thanks!

The only part I don't understand is the current on the middle block (and hence, the force on the middle block). I get the first and third parts.

Thanks!

Okay, for part b, where the loop is traveling entirely within the field, consider the situation where you connect two identical batteries together in parallel: positive terminal to positive terminal, and negative terminal to negative terminal (with no other connections made). Is there any current?

 

[skibum143]

No...current has to go from hi to low, or positive to negative. So there is no current.