Magnetic Field of an AA Battery 'Immersed' in a Conductor

[Fibonacci Vonacci]

If an AA battery were placed in some kind of ideal conducting 'ether':

1) Would current flow, and if so, what would the flow of electrons look like?

2) How would the magnetic field look? (I imagine that if there was an electric current flowing, that the magnetic field would look a little like the magnetic field of the earth)

3) If placed near another magnetic field would the battery 'roll' towards the new source?

 

[davenn]

some kind of ideal conducting 'ether':

what is that ??
without being able to define this mythical substance, none of the rest of your questions make any sense

 

[Fibonacci Vonacci]

what is that ??
without being able to define this mythical substance, none of the rest of your questions make any sense

I do not have enough knowledge to define such a substance, so perhaps I can ask it in a different way, starting with a first step.

As a thought experiment, is it theoretically conceivable that a substance could exist with the properties that it could surround a battery allowing current to flow through itself?

 

[CWatters]

Water could be considered a "conducting ether" just not a very good one.

 

[Fibonacci Vonacci]

Water could be considered a "conducting ether" just not a very good one.

Yes indeed, in water it is the impurities that conduct electricity. I'm hoping to grasp what an ideal conducting medium might act like in this model, so I suppose 'ideal' needs some clarification. To my beginner's mind this might mean that the electrons are free to move in any direction, so that resistance is uniform.

I appreciate that what I asked may be absurd, but when asking it I do not know enough to know why it is absurd.

 

[CWatters]

Ok so I think this is like putting the battery in a thick walled tubular conductor with the paper wrapper on the battery forming a void. So perhaps see some of the digrams here...

https://www.nde-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/CircularFields.htm

 

[Spinnor]

Water could be considered a "conducting ether" just not a very good one.

Add some salt.

 

[Spinnor]

1) Would current flow, and if so, what would the flow of electrons look like?

Let the battery be in the middle of a large saltwater pool. The flow will be symmetric about the axis of the battery? The flow will be most intense near the battery? Far from the battery the flow is small but not zero?

What is the differential form of Ohm's law for 3 dimensional conductors like our case above?

Thanks!

 

[tech99]

If an AA battery were placed in some kind of ideal conducting 'ether':

1) Would current flow, and if so, what would the flow of electrons look like?

2) How would the magnetic field look? (I imagine that if there was an electric current flowing, that the magnetic field would look a little like the magnetic field of the earth)

3) If placed near another magnetic field would the battery 'roll' towards the new source?

Looks like a coaxial cable, so nothing on the outside.

 

[Spinnor]

nothing on the outside

There will be current flow at large distances from the battery unlike a coax cable. Using this fact and the Biot-Savart Law you can show there must be a magnetic field.

 

[DrZoidberg]

If the whole arrangement is perfectly symmetric the magnetic field would also have to be symmetric around the battery. But according to maxwell's equations - more specifically Ampère's circuital law - that field needs to be zero here since the total electric current enclosed by the magnetic loop is zero.

 

[Spinnor]

the total electric current enclosed by the magnetic loop is zero.

Only if the loop is very large will the total current through the area of the loop be zero.

 

[Spinnor]

 

[Fibonacci Vonacci]

If the whole arrangement is perfectly symmetric the magnetic field would also have to be symmetric around the battery. But according to maxwell's equations - more specifically Ampère's circuital law - that field needs to be zero here since the total electric current enclosed by the magnetic loop is zero.

DrZoidberg, could you expand on this a little bit please? I'm struggling to understanding why the field needs to be zero.

 

[DrZoidberg]

Look at Spinnor's drawing. The field strength approaches zero if the loop is very large. Otherwise it's non zero.