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htg
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It is zero, contrary to published formulas. I assume that we are talking about a single wire, not about a twisted bunch of wires. Why is the misconception so popular?
htg said:it is zero, contrary to published formulas. I assume that we are talking about a single wire, not about a twisted bunch of wires. Why is the misconception so popular?
htg said:In usual circuits there is a return path, so you practically always have a loop, which actually has inductance.
A dipole has capacitance, which, when connected to proper inductance gives you an LC circuit, which resonates at certain frequency.
L = [itex]\Phi[/itex]/IThis note concerns the inductance of a straight wire. Surprisingly, it is not easy to find an expression for the inductance of a straight piece of wire, and it is far more difficult to find out how that expression was obtained. And yet this result is very useful as a building block for more complex structures, and also because the inductance of a wire is important in high frequency or high speed electrical circuits.
The first really convenient derivation of the inductance of a wire which I have been able to find is due to Rosa(1). The first dilemma which Rosa faced is that there is no unambiguous definition of how to define the inductance of a straight wire. If we consider the wire in isolation we ignore the question of how the current gets to the wire. But that current, however it is delivered, will affect the flux which is developed in the vicinity of the wire. But this flux is a part of the definition. Rosa resolved the dilemma arbitrarily (there is no other way) by defining the inductance as the ratio of the flux developed in the region bounded by lines perpendicular to the beginning and end of the wire. Let's look at Rosa's own words in which he recognizes the dilemma in the definition.
"I have derived the formulae in the simplest possible manner, using the law of Biot and Savart in the differential form instead of Neumann's equation, as it gives a better physical view of the various problems considered. This law has not, of course, been experimentally verified for unclosed circuits; but the self inductance of an unclosed circuit means simply its self-inductance as a part of a closed circuit, the total inductance of which cannot be determined until the entire circuit is specified. In this sense the use of the law of Biot and Savart to obtain the self-inductance of an unclosed circuit is perfectly legitimate."
One might question here what the word 'legitimate'. Rosa has made an assumption in order to obtain a result. That is fine, but I don't think you should say it is legitimate, in the sense of being according to law. There is no law to guide this assumption. In any event let us proceed to the solution. The approach is the following.
1. Set up the geometry of a point at some distance from a straight line.
2. Write dH from Biot Savart at that point. Let the current equal one for simplicity.
3. Find the total H due to all of the current in the line by integrating over the line.
4. Set B = uH.
5. Find the magnetic flux phi in a differential area which is parallel to the wire by integrating B over this area which is a fixed distance from the wire.
6. Find the total flux phi over all of the area from the edge of the wire to infinity by integrating over the distance from the wire to infinity.
7. Since the current was set equal to one, the total flux equals the inductance.
htg said:In usual circuits there is a return path, so you practically always have a loop, which actually has inductance.
To see why a straight wire has zero inductance, consider two charged balls, a switch - e.g. a MOSFET, and the straight wire. From the Biot-Savart-Laplace law you can calculate the magnetic field generated by the current in one part of the wire and see that it does not induce any voltage in another part of the wire.
jim hardy said:and i always figured that capacitance was the return path.
The directors & reflectors in a yagi will resonate unconnected to anything.
Inductance is flux linkages per ampere
and the amperes definitely flow
and i don't see why flux wouldn't link a straight conductor.
it's just counterintuitive, that's all.
truesearch said:My textbooks define self inductance in terms of induced emf/rate of change of current.
If the magnetic circuit has constant reluctance then this definition is equivalent to
L = flux linkage/current
?which post defined inductance?
htg said:In usual circuits there is a return path, so you practically always have a loop, which actually has inductance.
To see why a straight wire has zero inductance, consider two charged balls, a switch - e.g. a MOSFET, and the straight wire. From the Biot-Savart-Laplace law you can calculate the magnetic field generated by the current in one part of the wire and see that it does not induce any voltage in another part of the wire.
truesearch said:So it is confirmed that straight wires have an inductance of 1nH/mm.
How many employees do you have carlgrace?? How many have been fired because of their half-cocked theoretical ideas ?
Do you employ any 'theorists'; ??
I did employ people until a few years ago. Do you think that as soon as I took a position in academia I had to stop drawing conclusions based on my own previous experience?truesearch said:You do not employ anyone but you feel that you are in a position to determine who should be employed !
Yeah I apologized about that. I shouldn't have said that about theory.truesearch said:You are rude
I don't believe it is irrelevant. My point for saying that was showing there are a lot of pitfalls in trusting in "theory" too much. It has direct, specific consequences. TI became the world leader in transistor manufacturing because they chose not to buy into the contemporary state of semiconductor theory.truesearch said:Dont quote irrelevant facts about silicon transistors !
Yes, I can back it up. For example,truesearch said:"theory is extremely valuable" ... many here will value this statement
..."they don't necessarily "mean" anything, especially when there is contradictory experimental evidence available".
Can you back this up with hard evidence or is it a subjective, personal opinion?
truesearch said:Distractive truisms (eg deep submicronCmos technologyransistors (I just made that up !) should not be needed to disguise, back up, justify physics facts.
Physics is difficult but there is an awful amount of information available in standard textbooks. I wish that responses here were backed upwith textbook references.
Inductance is a property of an electrical circuit that describes the ability of the circuit to store energy in the form of a magnetic field. It is measured in units of Henrys (H).
The inductance of a straight wire can be calculated using the formula L = μ0*(N^2*A)/l, where L is the inductance, μ0 is the permeability of free space, N is the number of turns in the wire, A is the cross-sectional area, and l is the length of the wire.
The inductance of a straight wire is affected by the length and cross-sectional area of the wire, the number of turns in the wire, and the material the wire is made of. The presence of nearby conductors or magnetic materials can also affect the inductance.
Inductance can impact the functioning of a circuit in several ways. It can cause a delay in the flow of current, which can affect the timing of signals in the circuit. It can also create a back EMF (electromotive force) when the current in the circuit changes, which can affect the stability of the circuit.
Inductance is an important concept in the design of electrical circuits and is used in a variety of practical applications. It is used in the design of transformers, motors, generators, and other electromechanical devices. It is also used in electronic filters to control the flow of current and inductors are commonly used in power supplies to filter out unwanted high-frequency noise.