Okay fair enough. So then as long as the individual x, y and z components of the current vector of dl1 are multiplied with the respective x, y and z components of the current vector of dl2, and then the magnitudes of these three products are added together this will give the correct dot product...
While resistors don't "consume" voltage they do "drop" voltage. That is why I suggested using the voltage divider rule (substituting a resistance for the switch) and see what happens as you vary the bottom resistance from some finite value down to zero and then up to infinity.
I wouldn't call this amplification. To me that implies that you get out more energy than you put in, as would be the case with a powered audio amplifier. What you are doing is focusing (concentrating) the sound energy into a smaller space to make more efficient use of it.
Suggestion: Apply the voltage divider rule assuming the switch to be a resistor which can have one of two values (∞ or 0) depending on whether it's open or closed.
Hi Gabbagabbahey. Thank you for the explanation.
The detail that has me confused can probably be best illustrated in the following diagram:
In both cases, the elements dl1 and dl2 are parallel, and hence have the same direction cosines and therefore the same dot product. They are the same...
Not sure if you're looking for "complete" elliptic integrals or not. If you want the complete elliptic integrals of first and second kind, there's a very efficient algorithm using arithmetic-geometric means. I discuss it on my site, and have example code in Open Office Basic and Javascript...
I've been working my way through an old scientific paper on inductance calculation, and there's a fundamental principle I'm having a problem with.
Suppose there are two filamentary conductors of any arbitrary shape. Now consider an infinitesimal element dl1 somewhere on the first conductor...