Why is the magnetic field of a wire circular

[Entanglement]

The title is enough

 

[jtbell]

Look at the list of "Related Discussions" at the bottom of this thread, and you'll find two threads with the same question as yours. One of them has 24 responses, which looks promising!

 

[Entanglement]

Look at the list of "Related Discussions" at the bottom of this thread, and you'll find two threads with the same question as yours. One of them has 24 responses, which looks promising!

Could you please copy and paste these links in a reply because the mobile version doesn't allow make these links appear
Thanks very much

 

[Entanglement]

unfortunately, I couldn't get much from related discussions, could you provide a thorough explanation,
thanks in advance

 

[UltrafastPED]

It's an experimental observation, first made in 1820. See http://inventors.about.com/od/lessonplans/ht/magnetic_fields.htm

The Biot-Savart law was inspired by this and other observations.
See http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/biosav.html

So you should be able to start with the Biot-Savart law, and get back to Oersted's observation.

 

[WannabeNewton]

It's simply due to the cylindrical symmetry of the system.

 

[Entanglement]

It's an experimental observation, first made in 1820. See http://inventors.about.com/od/lessonplans/ht/magnetic_fields.htm

The Biot-Savart law was inspired by this and other observations.
See http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/biosav.html

So you should be able to start with the Biot-Savart law, and get back to Oersted's observation.

I know the observation, but I can't figure out its reason. Bio-Savarts law will only guide me to the direction of the field mathematically not logically nor intuitively.

 

[Entanglement]

It's simply due to the cylindrical symmetry of the system.

How isn't it a physics question if I want a deeper answer??

 

[UltrafastPED]

I know the observation, but I can't figure out its reason. Bio-Savarts law will only guide me to the direction of the field mathematically not logically nor intuitively.

Mathematics _is_ logic; and if you have a good intuition for geometry, you will do better with physical intuition as well.

 

[Entanglement]

Isn't there any other explanation, because bio-Savarts law is a way beyond my level b

 

[mfb]

What else than circular could it be? Do you expect rectangles? Why would you expect one direction from a straight wire look any different from other directions?

 

[Entanglement]

Why isn't there any poles
Why are the lines rotating around the wire and not ending or beginning at certain poles ?

 

[mikeph]

"Why" questions in physics are always so ill-posed.

Why not?
Can you answer that?

 

[UltrafastPED]

Why isn't there any poles
Why are the lines rotating around the wire and not ending or beginning at certain poles ?

Because magnetic fields don't originate from "magnetic charges". Thus they always go in a loop.

You see this if you have some iron filings (in a sealed plastic box) - as you bring any magnet close the filings will form an alignment which connects the poles.

If you stick two magnets together, N-S or N-N, you will see changes in the alignment, but always in a closed loop.

If you "break" a magnet it will always have two poles.

One of Maxwell's equations describes this behavior, but you will need to study vector calculus to understand the math; at this point simply try to understand what you are seeing, and how it changes with the experiment.


For example, what do you expect the magnetic field to look like if you bend the current carrying wire into a loop? Into a long coil?

 

[jtbell]

Here's an argument that the magnetic field around a straight wire has to be in circles simply because of the symmetry of the source:

https://www.physicsforums.com/showthread.php?p=4711973#post4711973

 

[Entanglement]

Here's an argument that the magnetic field around a straight wire has to be in circles simply because of the symmetry of the source:

https://www.physicsforums.com/showthread.php?p=4711973#post4711973

Thanks a lot !

 

[Entanglement]

Ampere Law states that

2\pir\Huge \propto I

\beta \propto I

2\pir\LARGE is the maximum circumference for the field??

 

[mfb]

2πr is just the exact circumference of a circle with radius r.
There is nothing "maximal". The (theoretical, ideal) field extends to infinity.

That is a weird way to reduce Ampere's law.

 

[Entanglement]

2πr is just the exact circumference of a circle with radius r.
There is nothing "maximal". The (theoretical, ideal) field extends to infinity.

That is a weird way to reduce Ampere's law.

What does it mean that circumference is directly proportional to the intensity ? Since there are infinite concentric circles

 

[mfb]

As I said, that is a weird way to reduce Ampere's law. You could read it "with larger current, you get the same field strength (which you omitted) at a larger radius".
And constant factors like 2π are irrelevant anyway if you look at proportional quantities.

 

[Entanglement]

As I said, that is a weird way to reduce Ampere's law. You could read it "with larger current, you get the same field strength (which you omitted) at a larger radius".
And constant factors like 2π are irrelevant anyway if you look at proportional quantities.

I think Br \propto I seems more meaningful
their product is directly proportional to the intensity

 

[Entanglement]

how is B at the center of a circular loop and a solenoid derived from :
Ampere's circular law
B = \muI / 2\pir

 

[mfb]

I think Br \propto I seems more meaningful
their product is directly proportional to the intensity

Yes.

B at the center of a circular loop is similar to a circular line around a straight wire. Both can be calculated from the more general Biot-Savart law.

 

[Entanglement]

how is B at the center of a circular loop and a solenoid derived from :
Ampere's circular law
B = \muI / 2\pir

?

 

[jtbell]

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c2

(which I found quickly via a Google search for "magnetic field at the center of a circular loop")

 

[Entanglement]

My Math Abd physics level doesn't allow me to understand bio-Savart's law isn't there any other way to understand via amperes law

 

[jtbell]

I don't think you can use Ampere's Law for this (magnetic field at the center of a circular loop). There isn't enough symmetry. I don't remember ever seeing this done using Ampere's Law.

However, you can use Ampere's Law to find B inside a long straight cylindrical solenoid, because of its symmetry:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html#c2

 

[mikeph]

You can use it. Take a surface integral of amperes law on a circle. Stokes theorem tells us the surface integral of the curl of B is equal to the line integral of the tangential magnetic field around the loop bounding the circle. From symmetry, the magnetic field cannot have any on the azimuth angle, so the local field can be derived using the radius of the circle.