How does looping a wire make it an inductor?

[Allan Davis]

Background: When electricity travels through a wire it creates a magnetic field around the wire. Creating the magnetic field requires energy, which is stored in the magnetic field.

So, if we have a length L of wire and wrap it in a small loop of say 100 turns, it becomes an air core inductor. However, as a straight wire it's not an inductor. How does looping it make it an inductor? Is the contribution of a small section of looped wire to the magnetic field of the inductor equal to the magnetic field surrounding the same small section of wire when it is straight? Or, does looping make the contribution of each small section greater than it would be if the wire is straight? Another way of phrasing the question is if current I is flowing through the wire of length L is the total energy in the surrounding magnetic field stronger when the wire is looped compared to when it is straight, and if it is, why?

 

[Dale]

However, as a straight wire it's not an inductor. How does looping it make it an inductor?

Hi Allan Davis, welcome to PF!

A straight wire does have inductance. In fact, calculating the inductance is a pretty common introductory exercise in EM classes.

Looping just makes the inductor more efficient.

 

[Allan Davis]

Hi Allan Davis, welcome to PF!

A straight wire does have inductance. In fact, calculating the inductance is a pretty common introductory exercise in EM classes.

Looping just makes the inductor more efficient.

Yes, that's what I"m wondering about. So the looped wire has more inductance than the straight wire? How or why does looping the wire around an air core make it more efficient?

Note: I found an inductance calculator and am studying the issue ! I see that looping the wire concentrates the magnetic field in the center to a strong aligned field.

But, it seems to me that the total energy in the magnetic field is the sum of the energies in the magnetic fields from each of the small segments of wire, and hence I don't see why it should be different when the wire is looped.

I keep editing ...
I think I'm getting it. When the wire is looped, the collapsing magnetic field in a small section of wire induces current in all the other wire segments that are adjacent to it, multiplying the current generated by collapsing magnetic field. So, the energy in the field would be the same whether the wire is straight or looped, but the current generated by a collapsing field will be greater when the wire is looped?

Note: I see I misspoke in my original post, I wrote 'as a straight wire it's not an inductor' where what I meant to write was 'as a straight wire it's not considered an inductor'.

 

[laner]

The main practical use of inductors is to resist changes in current in your circuit (ie: prevent voltage spikes, or act as one part of a band pass filter). You're definitely starting to get it with the change in current in the coil. Faradays law tells us that a changing magnetic flux through a loop of wire induces an EMF (Voltage) in that wire. Lenz's law tells us that the EMF produced will always drive a current in the direction that produces a magnetic field that opposes the change that caused the voltage spike in the first place. It sounds confusing but it can be summed up easily: whenever the magnetic flux through a surface bounded by a circuit changes, the circuit will respond by producing a magnetic field that tries to maintain the original direction and magnitude of magnetic flux, however it can.

So with regards to inductors, coils are ideal because the magnetic field produced by any single winding of the coil travels through the rest of the windings that make up the coil. The geometry is setup to be self-interacting. Imagine there is a voltage spike and the current increases very quickly. The increase in current causes increased magnetic flux throughout the coil. By Faradays/Lenz's law the inductor will produce a magnetic field that is opposed to this change (ie: the magnetic field produced by the inductor is opposite the direction of the magnetic field produced by the current spike). Now this magnetic field has to be caused by an EMF driving a current that is opposite the voltage spike. So this is how the inductor can dampen or prevent these types of sharp current changes. Whenever there is a spike in current the inductor always responds by producing a voltage that opposes the spike, because of how its geometry takes advantage of Faradays/Lenz's law.

Now consider the infinite straight wire with the same length as the inducting coil. It produces the same magnetic field per unit length, however the magnetic field is perpendicular to the wire at every point, so it never interacts with itself like in the coil case where the magnetic field travels through the center of the coil. So the infinite straight wire can't oppose changes in voltage like the coil can because Faradays law is not applicable in the same way.

Hopefully that helps. It's all just generalized right hand rule stuff.

 

[NascentOxygen]

Yes, that's what I"m wondering about. So the looped wire has more inductance than the straight wire? How or why does looping the wire around an air core make it more efficient?

Each loop is influenced by not only the flux lines it produces, but also by the flux from the current in all of the other loops around it, the effect diminishing with separation.

(I see you basically wrote this, now.)

Note: I see I misspoke in my original post, I wrote 'as a straight wire it's not an inductor' where what I meant to write was 'as a straight wire it's not considered an inductor'.

A straight wire is considered to have inductance that can't be ignored when its length is significant compared to the wavelength involved, e.g., at power line frequencies this means long transmission lines, but at microwave frequencies just a centimetre or two.

 

[davenn]

How or why does looping the wire around an air core make it more efficient?

because you are concentrating the magnetic field into a smaller area

 

[tech99]

because you are concentrating the magnetic field into a smaller area

Yes, into a smaller volume, and each turn of wire now falls within the magnetic field from its neighbours.