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What does a fairy have to do with magnetic reluctance? Just an analogy to our economy and news media.
If you watched CNN a couple of nights ago you might have seen Erin Burnett pretend to interview some congressman, I forget who, allowing him to invoke the confidence fairy unchallenged. The idea is that in times such as these, the government must practice austerity because that will give industry the confidence to start producing more, thus creating jobs. This works neither in theory nor practice. Industry produces more when it has good reason to believe it can sell what it produces. This requires money in the hands of the consumer.
She also did not challenge his moronic assertion that you cannot raise the taxes on the rich (back to where they were in 2000) because it is their spending that keeps the economy going. Orders for yachts, and all that. Well, we all know that one characteristic of wealth is having more money than you need for immediate purchases. Raising taxes on the wealthy does not cut their spending that much. If you want to increase spending and get the economy moving, make sure those who are not wealthy have the bucks. They will spend them because they really need what they buy.
These two fallacies are seen regularly in our news media, especially FOX.
On this forum we have a similar situation with the reluctance fairy. Several people here often invoke this little demon in order to explain how pickups work.
The intuitive appeal for the concept of magnetic circuits is this: understand ohm"s law (E = IR) and also understand how circuits using magnetism work. It is only this simple in certain special cases, and the guitar pickup is not one of them. As explained here: Magnetic circuit - Wikipedia, the free encyclopedia, the more general analogy is between B = (mu)H and J = (sigma)E.
The first equation means that if we set up an H field by establishing a system of currents, then the magnetic field at each point in space is determined by multiplying this field at each point by the permeability of the material at each point, including free space, which has a finite, but low, permeability. The second equation means that the current density at any point in space is given by the conductivity times the electric field.
These equations have the same form, and it is true that solving one also solves a problem that applies to the other. However, both are more complicated than they look because of the underlying physics. For example, in general you know the conductivity at the beginning of problem, but you know neither the E field nor the current density. This is because the E field depends on the spatial change of the charge density, and currents move charge around. You have to seek a self-consistent solution to a differential equation.
Neither equation is easier to solve than the other. A program such as FEMM, which solves the magnetic problem numerically also can be used to solve the electric problem.
The simple form of the reluctance analogy using ohm's law works only when you have a tightly coupled circuit with very little leakage flux. An example is a steel core transformer with an enclosed core except for an air gap. The air gap has high reluctance, the steel low, and the reluctance around the circuit is given to a good approximation by the air, and can be computed easily. Using an analogy to the voltage source, one can compute the flux. Then you have what you need in order to apply the law of magnetic induction.
Notice that last sentence: using reluctance does not replace the law of magnetic induction, it merely makes it easy to use in this case by helping you determine the flux.
Now consider the pickup. We have open cores of magnetic material sitting in free space with a small bit of magnetic material over one end of each core (a section of the string). One can consider the circuit composed of flux passing through a core (and thus through the coil) and the string. But there is no easy way to compute the flux passing through the core and how it changes as the string moves. You simply have to solve the differential equation. And in doing so you recognize that there are a large steady field and a small varying one. You want the small varying one that is a result of the vibrating string. You find that by using the large steady field that the string sits in and its permeability. And then you solve for the changing field through the core.
But what you never do is use the concept of variable reluctance as a source for intuitive ideas of how a pickup works. That is complete nonsense. Variable reluctance is a strictly mathematical analogy between similar equations. It has nothing to do with the intuitive understanding of the physics of pickups. For that you simply must understand the equations describing electromagnetism. You never invoke the reluctance fairy; the little devil is just going to confound you and make you believe things that are not true.
If you watched CNN a couple of nights ago you might have seen Erin Burnett pretend to interview some congressman, I forget who, allowing him to invoke the confidence fairy unchallenged. The idea is that in times such as these, the government must practice austerity because that will give industry the confidence to start producing more, thus creating jobs. This works neither in theory nor practice. Industry produces more when it has good reason to believe it can sell what it produces. This requires money in the hands of the consumer.
She also did not challenge his moronic assertion that you cannot raise the taxes on the rich (back to where they were in 2000) because it is their spending that keeps the economy going. Orders for yachts, and all that. Well, we all know that one characteristic of wealth is having more money than you need for immediate purchases. Raising taxes on the wealthy does not cut their spending that much. If you want to increase spending and get the economy moving, make sure those who are not wealthy have the bucks. They will spend them because they really need what they buy.
These two fallacies are seen regularly in our news media, especially FOX.
On this forum we have a similar situation with the reluctance fairy. Several people here often invoke this little demon in order to explain how pickups work.
The intuitive appeal for the concept of magnetic circuits is this: understand ohm"s law (E = IR) and also understand how circuits using magnetism work. It is only this simple in certain special cases, and the guitar pickup is not one of them. As explained here: Magnetic circuit - Wikipedia, the free encyclopedia, the more general analogy is between B = (mu)H and J = (sigma)E.
The first equation means that if we set up an H field by establishing a system of currents, then the magnetic field at each point in space is determined by multiplying this field at each point by the permeability of the material at each point, including free space, which has a finite, but low, permeability. The second equation means that the current density at any point in space is given by the conductivity times the electric field.
These equations have the same form, and it is true that solving one also solves a problem that applies to the other. However, both are more complicated than they look because of the underlying physics. For example, in general you know the conductivity at the beginning of problem, but you know neither the E field nor the current density. This is because the E field depends on the spatial change of the charge density, and currents move charge around. You have to seek a self-consistent solution to a differential equation.
Neither equation is easier to solve than the other. A program such as FEMM, which solves the magnetic problem numerically also can be used to solve the electric problem.
The simple form of the reluctance analogy using ohm's law works only when you have a tightly coupled circuit with very little leakage flux. An example is a steel core transformer with an enclosed core except for an air gap. The air gap has high reluctance, the steel low, and the reluctance around the circuit is given to a good approximation by the air, and can be computed easily. Using an analogy to the voltage source, one can compute the flux. Then you have what you need in order to apply the law of magnetic induction.
Notice that last sentence: using reluctance does not replace the law of magnetic induction, it merely makes it easy to use in this case by helping you determine the flux.
Now consider the pickup. We have open cores of magnetic material sitting in free space with a small bit of magnetic material over one end of each core (a section of the string). One can consider the circuit composed of flux passing through a core (and thus through the coil) and the string. But there is no easy way to compute the flux passing through the core and how it changes as the string moves. You simply have to solve the differential equation. And in doing so you recognize that there are a large steady field and a small varying one. You want the small varying one that is a result of the vibrating string. You find that by using the large steady field that the string sits in and its permeability. And then you solve for the changing field through the core.
But what you never do is use the concept of variable reluctance as a source for intuitive ideas of how a pickup works. That is complete nonsense. Variable reluctance is a strictly mathematical analogy between similar equations. It has nothing to do with the intuitive understanding of the physics of pickups. For that you simply must understand the equations describing electromagnetism. You never invoke the reluctance fairy; the little devil is just going to confound you and make you believe things that are not true.
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